eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-08-01
11
1
1
11
10.22130/scma.2018.68276.261
32195
مقاله پژوهشی
Coherent Frames
Ataollah Askari Hemmat
askari@mail.uk.ac.ir
1
Ahmad Safapour
safapour@vru.ac.ir
2
Zohreh Yazdani Fard
zohreh.yazdanifard@gmail.com
3
Department of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O.Box 76169-133, Kerman, Iran.
Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.
Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.
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
http://scma.maragheh.ac.ir/article_32195_afa7e7e72abfe740af573ccc4c15cbac.pdf
Coherent frame
Continuous frame
Locally compact group
Unitary representation
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-08-01
11
1
13
23
10.22130/scma.2018.72221.284
32215
مقاله پژوهشی
On Polar Cones and Differentiability in Reflexive Banach Spaces
Ildar Sadeqi
esadeqi@sut.ac.ir
1
Sima Hassankhali
s-hassankhali@sut.ac.ir
2
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
Let $X$ be a Banach space, $Csubset X$ 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 ${mathop{rm int}}(mathrm{dom} sigma_C) neqemptyset$. 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 ${mathop{rm int}}(mathrm{dom} sigma_C)$.
http://scma.maragheh.ac.ir/article_32215_2e744dde303f4e6c175af724da107e48.pdf
Recession cone
Polar cone
Bounded base
Support function
Gateaux differentiability
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-08-01
11
1
25
41
10.22130/scma.2018.60715.215
31436
مقاله پژوهشی
Meir-Keeler Type Contraction Mappings in $c_0$-triangular Fuzzy Metric Spaces
Masoomeh Hezarjaribi
hezarjaribimasoomeh@gmail.com
1
Department of Mathematics, Payame Noor University, p.o.box.19395-3697, Tehran, Iran.
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 $alphaDelta$-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.
http://scma.maragheh.ac.ir/article_31436_7931223a921acacbf9af5f50b37f2216.pdf
$c_0$-triangular fuzzy metric space
$alphaDelta$-Meir-Keeler contractive
Fixed point
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-08-01
11
1
43
63
10.22130/scma.2017.27953
27953
مقاله پژوهشی
On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions
Sanjib Kumar Datta
sanjib_kr_datta@yahoo.co.in
1
Tanmay Biswas
tanmaybiswas_math@rediffmail.com
2
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
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.
http://scma.maragheh.ac.ir/article_27953_14efa717fdebe100e756052a42d77176.pdf
Entire function
Generalized relative order
Generalized relative lower order
Generalized relative type
Generalized relative weak type
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-08-01
11
1
65
79
10.22130/scma.2018.74231.310
32196
مقاله پژوهشی
$G$-dual Frames in Hilbert $C^{*}$-module Spaces
Fatemeh Ghobadzadeh
gobadzadehf@yahoo.com
1
Abbas Najati
a.nejati@yahoo.com
2
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
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.
http://scma.maragheh.ac.ir/article_32196_3364381d248abfc90aba70ebe0afb964.pdf
Frame
$g$-dual frame
Hilbert $C^{*}$-module
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-08-01
11
1
81
89
10.22130/scma.2018.52976.155
31379
مقاله پژوهشی
Some Fixed Point Results for the Generalized $F$-suzuki Type Contractions in $b$-metric Spaces
Sumit Chandok
sumit.chandok@thapar.edu
1
Huaping Huang
mathhhp@163.com
2
Stojan Radenović
radens@beotel.net
3
School of Mathematics, Thapar University, Patiala-147004, India.
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China.
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.
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.
http://scma.maragheh.ac.ir/article_31379_085d0dfa121b0af90091cb95f787a50b.pdf
Fixed point
Generalized $F$-Suzuki contraction
$b$-metric space
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-08-01
11
1
91
97
10.22130/scma.2017.23702
23702
مقاله پژوهشی
Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras
Fatemeh Golfarshchi
f.golfarshchi@tabriziau.ac.ir
1
Ali Asghar Khalilzadeh
khalilzadeh@sut.ac.ir
2
Department of Multimedia, Tabriz Islamic Art University, Tabriz, Iran.
Department of Mathematics, Sahand University of Technology, Sahand Street, Tabriz, Iran.
Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ 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 $A$.
http://scma.maragheh.ac.ir/article_23702_316d0365f3c8803a7c76c12c9e348c05.pdf
$C^{*}$-algebra
Hilbert $C^{*}$-module
Invertibility preserving
Spectral radius preserving
Jordan isomorphism
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-08-01
11
1
99
113
10.22130/scma.2017.28506
28506
مقاله پژوهشی
A Coupled Random Fixed Point Result With Application in Polish Spaces
Rashwan Ahmed Rashwan
rashwan10@gmail.com
1
Hasanen Abuel-Magd Hammad
2
Department of Mathematics, Faculty of Science, Assuit University, Assuit 71516, Egypt.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
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.
http://scma.maragheh.ac.ir/article_28506_00489e0591464d632713e87b210c626a.pdf
Coupled random fixed point
$varphi $-contraction
Polish space
Random nonlinear integral equations
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-08-01
11
1
115
132
10.22130/scma.2018.63445.240
31559
مقاله پژوهشی
The Integrating Factor Method in Banach Spaces
Josefina Alvarez
jalvarez@nmsu.edu
1
Carolina Espinoza-Villalva
carolina.espinoza@mat.uson.mx
2
Martha Guzman-Partida
martha@mat.uson.mx
3
Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003, USA.
Departamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.
Departamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.
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.
http://scma.maragheh.ac.ir/article_31559_3d3a29c3ca9569969a1733143533626c.pdf
Banach spaces
Cauchy-Riemann integral
Exponential function
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-08-01
11
1
133
143
10.22130/scma.2018.61252.220
31813
مقاله پژوهشی
Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions
Arzu Akgul
akgulcagla@hotmail.com
1
Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli, Turkey.
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].
http://scma.maragheh.ac.ir/article_31813_4b05488564ecc7fb962eff344c90a60f.pdf
Analytic functions
Univalent functions
Bi-univalent functions
Taylor-Maclaurin series
Koebe function
Starlike and convex functions
Coefficient bounds
Polylogarithm functions