ORIGINAL_ARTICLE
Coherent Frames
Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $\mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of a single element of Hilbert space $\mathcal{H}$ under some unitary representation $\pi$ of $G$ on $\mathcal{H}$. It is interesting that most of important frames are coherent. We investigate canonical dual and combinations of this frames
https://scma.maragheh.ac.ir/article_32195_afa7e7e72abfe740af573ccc4c15cbac.pdf
2018-08-01
1
11
10.22130/scma.2018.68276.261
Coherent frame
Continuous frame
Locally compact group
Unitary representation
Ataollah
Askari Hemmat
askari@mail.uk.ac.ir
1
Department of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O.Box 76169-133, Kerman, Iran.
AUTHOR
Ahmad
Safapour
safapour@vru.ac.ir
2
Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.
AUTHOR
Zohreh
Yazdani Fard
zohreh.yazdanifard@gmail.com
3
Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.
LEAD_AUTHOR
[1] S.T. Ali, J.P. Antoine, and J.P. Gazeau, Continuous frames in Hilbert spaces, Ann. Phys., 222 (1993), pp. 1-37.
1
[2] J.P. Antoine and P. Vandergheynst, Wavelets on 2-Sphere: a Group Theoretical Approach, Appl. Comput. Harmon. Anal., 7 (1999), pp. 1-30.
2
[3] M. Azhini and M. Beheshti, Some results on continuous frames for Hilbert Spaces, Int. J. Industrial Mathematics, 2 (2001), pp. 37-42.
3
[4] P. Balazs and P.D.T. Stoven, Representation of the inverse of a frame multiplier, J. Math. Anal. Appl., 422 (2015), pp. 981-994.
4
[5] H. Bölcskel, F. Hlawatsch, and H.G. Feichtinger, Frame-theoretic analysis of oversampled filter banks, IEEE Trans. Signal Process., 46 (1998), pp. 3256-3268.
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[6] E.J. Candès and D. Donoho, New tight frames of curvelets and optimal representations of objects with piecewise $C^2$ singularities, Comm. Pure and Appl. Math., 56 (2004), pp. 216-266.
6
[7] P.G. Casazza and G. Kutyniok, Finite Frames: Theory and Applications, Birkhäuser, Boston, 2012.
7
[8] O. Chritensen, An Introduction to Frames and Riesz Bases, Birkhäuser, Boston, 2002.
8
[9] I. Daubechies, A. Grasmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 1271-1283.
9
[10] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341-366.
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[11] G.B. Folland, A Course in abstract harmonic analysis, CRC Press, Florida, 1995.
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[12] D. Gabor, Theory of communication, J. Inst. Electr. Eng. London, 93 (1946), pp. 429-457.
12
[13] K. Grächening, The homogeneous approximation property and the comparison theorem for coherent frames, sampl. Theory Signal Image Process., 7 (2008), pp. 271-279.
13
[14] D. Han and D.R. Larson, Frames, Bases, and Group Representations, Mem. Amer. Math. Soc., 147 (2000), pp. 1-94.
14
[15] R.W. Heath and A.J. Paulraj, Linear dispersion codes for MIMO systems based on frame theory, IEEE Trans. Signal Process., 50 (2002), pp. 2429-2441.
15
[16] G. Kaiser, A Friendly Guide to Wavelets, Birkhäuser, Boston, 1994.
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[17] R.V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras, Vol. I, Academic Press, New York, 1983.
17
[18] A. Rahimi, A. Najati, and Y.N. Dehghan, Continuous frames in Hilbert spaces, Meth. Func. Anal. Top., 12 (2006), pp. 170-182.
18
ORIGINAL_ARTICLE
On Polar Cones and Differentiability in Reflexive Banach Spaces
Let $X$ be a Banach space, $C\subset X$ be a closed convex set included in a well-based cone $K$, and also let $\sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set $C$, so that ${\mathop{\rm int}}(\mathrm{dom} \sigma_C) \neq\emptyset$. The latter is a primary condition for subdifferentiability of the support function $\sigma_C$. Eventually, we study Gateaux differentiability of support function $\sigma_C$ on two sets, the polar cone of $K$ and ${\mathop{\rm int}}(\mathrm{dom} \sigma_C)$.
https://scma.maragheh.ac.ir/article_32215_2e744dde303f4e6c175af724da107e48.pdf
2018-08-01
13
23
10.22130/scma.2018.72221.284
Recession cone
Polar cone
Bounded base
Support function
Gateaux differentiability
Ildar
Sadeqi
esadeqi@sut.ac.ir
1
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
LEAD_AUTHOR
Sima
Hassankhali
s-hassankhali@sut.ac.ir
2
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
AUTHOR
[1] C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd Edition, Springer-Verlag, Berlin, 2006.
1
[2] J.M. Borwein and J.D. Vanderwerff, Convex functions: constructions, characterizations and counterexamples, Encyclopedia of Mathematics and its Applications, 109. Cambridge. Univ. Press, Cambridge, 2010.
2
[3] E. Casini and E. Miglierina, Cones with bounded and unbounded bases and reflexivity, Nonlinear Anal., 72 (2010), pp. 2356-2366.
3
[4] M. Fabian, P. Habala, P. Hajek, V. Montesinos, and V. Zizler, Banach space theory, the basis for linear and unlinear analysis, CMS Books in Math, Springer, Canada, 2011.
4
[5] Z.Q . Han, Relationship between solid cones and cones with bases, Optim. Theory Appl., 90 (1996), pp. 457-463.
5
[6] Z.Q. Han, Remarks on the angle poperty and solid cones, J. Optim. Theory Appl. 82 (1994), pp. 149-157.
6
[7] G. Isac, Pareto optimization in infinite-dimensional spaces, the importance of nuclear cones, J. Math. Anal. Appl., 182 (1994), pp. 393-404.
7
[8] J. Jahn, Vector optimization theorem, theory, application and existence, Springer, Verlag Berlin Heidelberg, 2011.
8
[9] A. Khan, Ch. Christiane, and C. Zalinescu, Set-valued Optimization, An introduction with application, Springer, Verlag Berlin Heidelberg, 2015.
9
[10] I.A . Polyrakis, Demand functions and reflexivity, J. Math. Anal. Appl., 338 (2008), pp. 695-704.
10
[11] J.H. Qiu, On Solidness of Polar Cones, J. Optim. Theory Appl., 109 (2001), pp. 199–214.
11
ORIGINAL_ARTICLE
Meir-Keeler Type Contraction Mappings in $c_0$-triangular Fuzzy Metric Spaces
Proving fixed point theorem in a fuzzy metric space is not possible for Meir-Keeler contractive mapping. For this, we introduce the notion of $c_0$-triangular fuzzy metric space. This new space allows us to prove some fixed point theorems for Meir-Keeler contractive mapping. As some pattern we introduce the class of $\alpha\Delta$-Meir-Keeler contractive and we establish some results of fixed point for such a mapping in the setting of $c_0$-triangular fuzzy metric space. An example is furnished to demonstrate the validity of these obtained results.
https://scma.maragheh.ac.ir/article_31436_7931223a921acacbf9af5f50b37f2216.pdf
2018-08-01
25
41
10.22130/scma.2018.60715.215
$c_0$-triangular fuzzy metric space
$alphaDelta$-Meir-Keeler contractive
Fixed point
Masoomeh
Hezarjaribi
hezarjaribimasoomeh@gmail.com
1
Department of Mathematics, Payame Noor University, p.o.box.19395-3697, Tehran, Iran.
LEAD_AUTHOR
[1] C. Di Bari and C. Vetro, A fixed point theorem for a family of mappings in a fuzzy metric space, Rend. Circ. Mat. Palermo, 52 (2003), pp. 315-321.
1
[2] C. Di Bari and C. Vetro, Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math., 13 (2005), pp. 973-982.
2
[3] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), pp. 395-399.
3
[4] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), pp. 385-389.
4
[5] J. Jachymski, Equivalent condition and the Meir-Keeler type theorems , J. Math. Anal. Appl., 194 (1995), pp. 293-303.
5
[6] E. Karapinar, P. Kumam, and P. Salimi, On $alpha$$-psi$-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 1 (2013), pp. 1-12.
6
[7] I. Kramosil and J. Michálek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), pp. 336-344.
7
[8] A. Meir and E. Keeler, A theorem on contraction mapping, J. Math. Anal. Appl., 28 (1969), pp. 326-329.
8
[9] S. Park and B.E. Rhoades, Meir-Keeler type contractive condition, Math. Japon., 26 (1981), pp. 13-20.
9
[10] A.C.M. Ran and M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), pp. 1435-1443.
10
[11] B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for $alpha$$-psi$-contractive type mappings, Nonlinear Anal., 75 (2012), pp. 2154-2165.
11
[12] Y.Shen, D.Qiu, and W.Chenc, Fixed point theorems in fuzzy metric spaces, Appl. Math. Letters, 25 (2012), pp. 138-141.
12
[13] L.A. Zadeh, Fuzzy sets, Information & Control, 8 (1965), pp. 338-353.
13
ORIGINAL_ARTICLE
On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions
In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.
https://scma.maragheh.ac.ir/article_27953_14efa717fdebe100e756052a42d77176.pdf
2018-08-01
43
63
10.22130/scma.2017.27953
Entire function
Generalized relative order
Generalized relative lower order
Generalized relative type
Generalized relative weak type
Sanjib
Kumar Datta
sanjib_kr_datta@yahoo.co.in
1
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
LEAD_AUTHOR
Tanmay
Biswas
tanmaybiswas_math@rediffmail.com
2
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
AUTHOR
[1] L. Bernal, Crecimiento relativo de funciones enteras. Contribucion al estudio de lasfunciones enteras conindice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.
1
[2] L. Bernal, Orden relative de crecimiento de funciones enteras, Collect. Math., Vol. 39 (1988), pp. 209-229.
2
[3] S.K. Datta and T. Biswas, Growth of entire functions based on relative order, Int. J. Pure Appl. Math., Vol. 51, No. 1 (2009), pp. 49-58.
3
[4] S.K. Datta and A. Biswas, On relative type of entire and meromorphic functions, Advances in Applied Mathematical Analysis, Vol. 8, No. 2 (2013), pp. 63-75.
4
[5] S.K. Datta and T. Biswas, Relative order of composite entire functions and some related growth properties, Bull. Cal. Math. Soc., Vol. 102, No.3 (2010) pp.259-266.
5
[6] S.K. Datta, T. Biswas and R. Biswas, Comparative growth properties of composite entire functions in the light of their relative order, The Mathematics Student, Vol. 82, No. 1-4 (2013), pp. 1-8.
6
[7] S.K. Datta, T. Biswas, and R. Biswas, On relative order based growth estimates of entire functions, International J. of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 7, No. II (March, 2013), pp. 59-67.
7
[8] S.K. Datta, T. Biswas, and D.C. Pramanik, On relative order and maximum term -related comparative growth rates of entire functions, Journal of Tripura Mathematical Society, Vol. 14 (2012), pp. 60-68.
8
[9] S.K. Datta, T. Biswas, and C. Ghosh, Growth analysis of entire functions concerning generalized relative type and generalized relative weak type, Facta Universitatis (NIS) Ser. Math. Inform, Vol. 30, No. 3 (2015), pp. 295-324.
9
[10] S.K. Datta and A. Jha, On the weak type of meromorphic functions, Int. Math. Forum, Vol. 4, No. 12(2009), pp. 569-579.
10
[11] B.K. Lahiri and D. Banerjee, Generalised relative order of entire functions, Proc. Nat. Acad. Sci. India, Vol. 72(A), No. IV (2002), pp. 351-271.
11
[12] C. Roy, Some properties of entire functions in one and several complex variables, Ph.D. Thesis, submitted to University of Calcutta, 2009.
12
[13] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., Vol. 69 (1963), pp. 411-414.
13
[14] E.C. Titchmarsh, The theory of functions, 2nd ed. Oxford University Press, Oxford, (1968).
14
[15] G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, (1949).
15
ORIGINAL_ARTICLE
$G$-dual Frames in Hilbert $C^{*}$-module Spaces
In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames are given. A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is not satisfied in general Hilbert $C^*$-modules.
https://scma.maragheh.ac.ir/article_32196_3364381d248abfc90aba70ebe0afb964.pdf
2018-08-01
65
79
10.22130/scma.2018.74231.310
Frame
$g$-dual frame
Hilbert $C^{*}$-module
Fatemeh
Ghobadzadeh
gobadzadehf@yahoo.com
1
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
AUTHOR
Abbas
Najati
a.nejati@yahoo.com
2
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
LEAD_AUTHOR
[1] P. Balazs and D.T. Stoeva, Representation of the inverse of a frame multiplier, J. Math. Anal. Appl., 422 (2015), pp. 981-994.
1
[2] O. Christensen and R.S. Laugesen, Approximately dual frame pairs in Hilbert spaces and applications to Gabor frames, Sampl. Theory Signal Image Process. 9 (2010), pp. 77-89.
2
[3] M.A. Dehghan and M.A. Hasankhani Fard, $G$-dual frames in Hilbert spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 75 (2013), pp. 129-140.
3
[4] L. Dengfeng and L. Yanting, $G$-dual frames for generalized frames, Adv. Math., (China), 45 (2016), pp. 919-931.
4
[5] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341-366.
5
[6] M. Frank and D.R. Larson, Frames in Hilbert $C^*$-modules and $C^*$-algebras, J. Operator Theory, 48 (2002), pp. 273-314.
6
[7] M. Frank and D.R. Larson, A module frame concept for Hilbert $C^*$-modules, The functional and harmonic analysis of wavelets and frames (San Antonio, TX, 1999), 207--233, Contemp. Math., 247, Amer. Math. Soc., Providence, RI, 1999.
7
[8] F. Ghobadzadeh, A. Najati, G.A. Anastassiou, and C. Park, Woven frames in Hilbert $C^*$-module spaces, J. Comput. Anal. Appl., 25 (2018), pp. 1220-1232.
8
[9] F. Ghobadzadeh, A. Najati, and E. Osgooei, Modular frames and invertibility of multipliers in Hilbert $C^*$-modules, (submitted).
9
[10] D. Han, D. Larson, W. Jing, and R.N. Mohapatra, Riesz bases and their dual modular frames in Hilbert $C^*$-modules, J. Math. Anal. Appl., 343 (2008), pp. 246-256.
10
[11] M.A. Hasankhanifard and M.A. Dehghan, $G$-dual function-valued frames in $L^2(0,$∞$)$, Wavel. Linear Algebra, 2 (2015), pp. 39-47.
11
[12] H. Javanshiri, Some properties of approximately dual frames in Hilbert spaces, Results Math., 70 (2016), pp. 475-485.
12
[13] E.C. Lance, Hilbert $C^*$-modules - a toolkit for operator algebraists, London Mathematical Society Lecture Note Series, vol. 210. Cambridge University Press, England, 1995.
13
[14] H. Li, A Hilbert $C^*$-module admitting no frames, Bull. London Math. Soc., 42 (2010), pp. 388-394.
14
[15] M. Mirzaee Azandaryani, Approximate duals and nearly Parseval frames, Turkish J. Math., 39 (2015), pp. 515-526.
15
[16] G.J. Murphy, $C^*$-algebras and operator theory, Academic Press, San Diego, 1990.
16
[17] A. Najati, M. Mohammadi Saem, and P. Guavruta, Frames and operators in Hilbert $C^*$-modules, Oper. Matrices, 10 (2016), 73-81.
17
[18] M. Rashidi-Kouchi, A. Nazari, and M. Amini, On stability of $g$-frames and $g$-Riesz bases in Hilbert $C^*$-modules, Int. J. Wavelets Multiresolut. Inf. Process., 12 (2014), pp. 1-16.
18
[19] M. Rashidi-Kouchi and A. Rahimi, Controlled frames in Hilbert $C^*$-modules, Int. J. Wavelets Multiresolut. Inf. Process., 15 (2017), pp. 1-15.
19
[20] D.T. Stoeva and P. Balazs, Invertibility of multipliers, Appl. Comput. Harmon. Anal., 33 (2012), pp. 292-299.
20
ORIGINAL_ARTICLE
Some Fixed Point Results for the Generalized $F$-suzuki Type Contractions in $b$-metric Spaces
Compared with the previous work, the aim of this paper is to introduce the more general concept of the generalized $F$-Suzuki type contraction mappings in $b$-metric spaces, and to establish some fixed point theorems in the setting of $b$-metric spaces. Our main results unify, complement and generalize the previous works in the existing literature.
https://scma.maragheh.ac.ir/article_31379_085d0dfa121b0af90091cb95f787a50b.pdf
2018-08-01
81
89
10.22130/scma.2018.52976.155
Fixed point
Generalized $F$-Suzuki contraction
$b$-metric space
Sumit
Chandok
sumit.chandok@thapar.edu
1
School of Mathematics, Thapar University, Patiala-147004, India.
AUTHOR
Huaping
Huang
mathhhp@163.com
2
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China.
LEAD_AUTHOR
Stojan
Radenović
radens@beotel.net
3
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.
AUTHOR
[1] M. Abbas, M. Berzig, T. Nazir, and E. Karapinar, Iterative approximation of fixed points for presic type $F$-contraction operators, Uni. Pol. Bucharest Sci. Bul. A-Appl. Math. Phy., 78 (2) (2016), pp. 147-160.
1
[2] H.H. Alsulami, E. Karapinar, and H. Piri, Fixed points of generalized F-Suzuki type contraction in complete $b$-metric spaces, Dis. Dyn. Nat. Soc., Volume 2015, Article ID 969726, 8 pages.
2
[3] H.H. Alsulami, E. Karapinar, and H. Piri, Fixed points of modified $F$-contractive mappings in complete metric-like spaces, J. Funct. Spaces, Volume 2015, Article ID 270971, 9 pages.
3
[4] I.A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal., 30 (1989), pp. 26-37.
4
[5] L. Ciric, S. Chandok, and M. Abbas, Invariant approximation results of generalized nonlinear contractive mappings, Filomat, 30 (2016), pp. 3875-3883.
5
[6] S. Czerwik, Contraction mappings in $b$-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), pp. 5-11.
6
[7] H. Ding, M. Imdad, S. Radenovic, and J. Vujakovic, On some fixed point results in $b$-metric, rectangular and $b$-rectangular metric spaces, Arab J. Math. Sci., 22 (2016), pp. 151-164.
7
[8] N.V. Dung, and V.L. Hang, A fixed point theorem for generalized $F$-contractions on complete metric spaces, Vietnam J. Math., 43 (2015), pp. 743-753.
8
[9] M. Jovanovic, Z. Kadelburg, and S. Radenovic, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., Volume 2010, Article ID 978121, 15 pages.
9
[10] E. Karapinar, M.A. Kutbi, H. Piri, and D. ORegan, Fixed points of conditionally $F$-contractions in complete metric-like spaces, Fixed Point Theory Appl., 2015 (2015), Article ID 126, 14 pages.
10
[11] H. Piri, and P. Kumam, Fixed point theorems for generalized $F$-Suzuki-contraction mappings in complete $b$-metric spaces, Fixed Point Theory Appl., 2016 (2016), Article ID 90, 13 pages.
11
[12] S. Shukla, S. Radenovic, and Z. Kadelburg, Some fixed point theorems for ordered $F$-generalized contractions in 0-$f$-orbitally complete partial metric spaces, Theory Appl. Math. Comput. Sci., 4 (2014), pp. 87-98.
12
[13] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), Article ID 94, 11 pages.
13
[14] D. Wardowski, and N.V. Dung, Fixed points of $F$-weak contractions on complete metric spaces, Demonstratio Math., 67 (2014), pp. 146-155.
14
ORIGINAL_ARTICLE
Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras
Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $\varphi:A\rightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $\varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.
https://scma.maragheh.ac.ir/article_23702_316d0365f3c8803a7c76c12c9e348c05.pdf
2018-08-01
91
97
10.22130/scma.2017.23702
$C^{*}$-algebra
Hilbert $C^{*}$-module
Invertibility preserving
Spectral radius preserving
Jordan isomorphism
Fatemeh
Golfarshchi
f.golfarshchi@tabriziau.ac.ir
1
Department of Multimedia, Tabriz Islamic Art University, Tabriz, Iran.
LEAD_AUTHOR
Ali Asghar
Khalilzadeh
khalilzadeh@sut.ac.ir
2
Department of Mathematics, Sahand University of Technology, Sahand Street, Tabriz, Iran.
AUTHOR
[1] B. Aupetit, Spectrum-preserving linear mappings between Banach algebras or Jordan-Banach algebras, J. Lond. Math Soc., 62 (2000) 917-924.
1
[2] B. Blackadar, Theory of $C^{*}$-algebras and Von Neumann algebras, Springer-Verlag, New York, 2006.
2
[3] M. Bresar and P. Semrl, Linear maps preserving the spectral radius, J. Funct. Anal., 142 (1996) 360-368.
3
[4] M. Bresar and P. Semrl, Invertibility preserving maps preserve idempotents, Michigan Math. J., 45 (1998) 483-488.
4
[5] A. Jafarian and A.R. Sourour, Spectrum preserving linear maps, J. Funct. Anal., 66 (1986) 255-261.
5
[7] E.C. Lance, Hilbert $C^{*}$-modules A toolkit for operator algebraists, Lond. Math. Soc., Lecture Notes Ser, 210, Cambridge University Press, Cambridge, 1995.
6
[8] M. Marcus and B.N. Moyls, Linear transformations on algebras of matrices, Canad. J. Math., 11 (1959) 61-66.
7
[9] M. Mathieu and A.R. Sourour, Hereditary properties of spectral isometries, Arch. Math., 82 (2004) 222-229.
8
[10] L. Molnar, Some characterizations of the automorphisms of $B(H)$ and $C(X)$, Proc. Amer. Math. Soc., 130 (2001) 111-120.
9
[11] J. Murphy, $C^{*}$-algebras and Operator Theory, Academic Press, Boston, 1990.
10
[12] S. Sakai, $C^{*}$-algebras and $W^{*}$-algebras, Springer-Verlag, New York, 1971.
11
[13] A.R. Sourour, Invertibility preserving linear maps on $L(X)$, Trans. Amer. Math. Soc., {348} (1996) 13-30.
12
[14] N.E. Wegge-Olsen, $K$-theory and $C^{*}$-algebras, Oxford University Press, New York, 1993.
13
ORIGINAL_ARTICLE
A Coupled Random Fixed Point Result With Application in Polish Spaces
In this paper, we present a new concept of random contraction and prove a coupled random fixed point theorem under this condition which generalizes stochastic Banach contraction principle. Finally, we apply our contraction to obtain a solution of random nonlinear integral equations and we present a numerical example.
https://scma.maragheh.ac.ir/article_28506_00489e0591464d632713e87b210c626a.pdf
2018-08-01
99
113
10.22130/scma.2017.28506
Coupled random fixed point
$varphi $-contraction
Polish space
Random nonlinear integral equations
Rashwan Ahmed
Rashwan
rashwan10@gmail.com
1
Department of Mathematics, Faculty of Science, Assuit University, Assuit 71516, Egypt.
LEAD_AUTHOR
Hasanen Abuel-Magd
Hammad
2
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
AUTHOR
[1] M. Abbas, M.A. Khan, and S. Radenovic, Common coupled fixed point theorems in cone metric spaces for w-compatible mapping, Appl. Math. Comput., 217 (2010) 195-202.
1
[2] M.U. Ali, T. Kamran, and M. Postolache, Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem, Nonlin. Anal. Modelling and Control, 22 (2017) 17-30.
2
[3] M.U. Ali and T. Kamran, Multivalued F-contraction and related fixed point theorems with application, Filomat, 30 (2016), 3779-3793.
3
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ORIGINAL_ARTICLE
The Integrating Factor Method in Banach Spaces
The so called integrating factor method, used to find solutions of ordinary differential equations of a certain type, is well known. In this article, we extend it to equations with values in a Banach space. Besides being of interest in itself, this extension will give us the opportunity to touch on a few topics that are not usually found in the relevant literature. Our presentation includes various illustrations of our results.
https://scma.maragheh.ac.ir/article_31559_3d3a29c3ca9569969a1733143533626c.pdf
2018-08-01
115
132
10.22130/scma.2018.63445.240
Banach spaces
Cauchy-Riemann integral
Exponential function
Josefina
Alvarez
jalvarez@nmsu.edu
1
Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003, USA.
AUTHOR
Carolina
Espinoza-Villalva
carolina.espinoza@mat.uson.mx
2
Departamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.
AUTHOR
Martha
Guzman-Partida
martha@mat.uson.mx
3
Departamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.
LEAD_AUTHOR
[1] A. Banner, The Calculus Lifesaver, Princeton University Press, New Jersey, 2007.
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ORIGINAL_ARTICLE
Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions
In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].
https://scma.maragheh.ac.ir/article_31813_4b05488564ecc7fb962eff344c90a60f.pdf
2018-08-01
133
143
10.22130/scma.2018.61252.220
Analytic functions
Univalent functions
Bi-univalent functions
Taylor-Maclaurin series
Koebe function
Starlike and convex functions
Coefficient bounds
Polylogarithm functions
Arzu
Akgul
akgulcagla@hotmail.com
1
Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli, Turkey.
LEAD_AUTHOR
[1] A. Akgul and S. Altinkaya, Coefficient estimates associated with a new subclass of bi-univalent functions, Acta Univ. Apulensis Math. Inform., 52 (2017), pp. 121-128
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Symmetric Points, J. Funct. Spaces, 2015 (2015), 5 pages.
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