University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
11
1
2018
08
01
Coherent Frames
1
11
EN
Ataollah
Askari Hemmat
Department of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O.Box 76169-133, Kerman, Iran.
askari@mail.uk.ac.ir
Ahmad
Safapour
0000-0002-8595-9565
Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.
safapour@vru.ac.ir
Zohreh
Yazdani Fard
Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.
zohreh.yazdanifard@gmail.com
10.22130/scma.2018.68276.261
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
Coherent frame,Continuous frame,Locally compact group,Unitary representation
https://scma.maragheh.ac.ir/article_32195.html
https://scma.maragheh.ac.ir/article_32195_afa7e7e72abfe740af573ccc4c15cbac.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
11
1
2018
08
01
On Polar Cones and Differentiability in Reflexive Banach Spaces
13
23
EN
Ildar
Sadeqi
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
esadeqi@sut.ac.ir
Sima
Hassankhali
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
s-hassankhali@sut.ac.ir
10.22130/scma.2018.72221.284
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 ${mathop{rm int}}(mathrm{dom} sigma_C)$.
Recession cone,Polar cone,Bounded base,Support function,Gateaux differentiability
https://scma.maragheh.ac.ir/article_32215.html
https://scma.maragheh.ac.ir/article_32215_2e744dde303f4e6c175af724da107e48.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
11
1
2018
08
01
Meir-Keeler Type Contraction Mappings in $c_0$-triangular Fuzzy Metric Spaces
25
41
EN
Masoomeh
Hezarjaribi
Department of Mathematics, Payame Noor University, p.o.box.19395-3697, Tehran, Iran.
hezarjaribimasoomeh@gmail.com
10.22130/scma.2018.60715.215
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.
$c_0$-triangular fuzzy metric space,$\alpha\Delta$-Meir-Keeler contractive,Fixed point
https://scma.maragheh.ac.ir/article_31436.html
https://scma.maragheh.ac.ir/article_31436_7931223a921acacbf9af5f50b37f2216.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
11
1
2018
08
01
On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions
43
63
EN
Sanjib
Kumar Datta
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
sanjib_kr_datta@yahoo.co.in
Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
tanmaybiswas_math@rediffmail.com
10.22130/scma.2017.27953
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.
Entire function,Generalized relative order,Generalized relative lower order,Generalized relative type,Generalized relative weak type
https://scma.maragheh.ac.ir/article_27953.html
https://scma.maragheh.ac.ir/article_27953_14efa717fdebe100e756052a42d77176.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
11
1
2018
08
01
$G$-dual Frames in Hilbert $C^{*}$-module Spaces
65
79
EN
Fatemeh
Ghobadzadeh
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
gobadzadehf@yahoo.com
Abbas
Najati
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
a.nejati@yahoo.com
10.22130/scma.2018.74231.310
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.
Frame,$g$-dual frame,Hilbert $C^{*}$-module
https://scma.maragheh.ac.ir/article_32196.html
https://scma.maragheh.ac.ir/article_32196_3364381d248abfc90aba70ebe0afb964.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
11
1
2018
08
01
Some Fixed Point Results for the Generalized $F$-suzuki Type Contractions in $b$-metric Spaces
81
89
EN
Sumit
Chandok
School of Mathematics, Thapar University, Patiala-147004, India.
sumit.chandok@thapar.edu
Huaping
Huang
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China.
mathhhp@163.com
Stojan
Radenović
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.
radens@beotel.net
10.22130/scma.2018.52976.155
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.
Fixed point,Generalized $F$-Suzuki contraction,$b$-metric space
https://scma.maragheh.ac.ir/article_31379.html
https://scma.maragheh.ac.ir/article_31379_085d0dfa121b0af90091cb95f787a50b.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
11
1
2018
08
01
Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras
91
97
EN
Fatemeh
Golfarshchi
Department of Multimedia, Tabriz
Islamic Art University, Tabriz, Iran.
f.golfarshchi@tabriziau.ac.ir
Ali Asghar
Khalilzadeh
Department of Mathematics, Sahand University of Technology, Sahand Street, Tabriz, Iran.
khalilzadeh@sut.ac.ir
10.22130/scma.2017.23702
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 $A$.
$C^{*}$-algebra,Hilbert $C^{*}$-module,Invertibility preserving,Spectral radius preserving,Jordan isomorphism
https://scma.maragheh.ac.ir/article_23702.html
https://scma.maragheh.ac.ir/article_23702_316d0365f3c8803a7c76c12c9e348c05.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
11
1
2018
08
01
A Coupled Random Fixed Point Result With Application in Polish Spaces
99
113
EN
Rashwan Ahmed
Rashwan
1234567892345678
Department of Mathematics, Faculty of Science, Assuit University, Assuit 71516, Egypt.
rashwan10@gmail.com
Hasanen Abuel-Magd
Hammad
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
10.22130/scma.2017.28506
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.
Coupled random fixed point,$varphi $-contraction,Polish space,Random nonlinear integral equations
https://scma.maragheh.ac.ir/article_28506.html
https://scma.maragheh.ac.ir/article_28506_00489e0591464d632713e87b210c626a.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
11
1
2018
08
01
The Integrating Factor Method in Banach Spaces
115
132
EN
Josefina
Alvarez
Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003, USA.
jalvarez@nmsu.edu
Carolina
Espinoza-Villalva
Departamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.
carolina.espinoza@mat.uson.mx
Martha
Guzman-Partida
Departamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.
martha@mat.uson.mx
10.22130/scma.2018.63445.240
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.
Banach spaces,Cauchy-Riemann integral,Exponential function
https://scma.maragheh.ac.ir/article_31559.html
https://scma.maragheh.ac.ir/article_31559_3d3a29c3ca9569969a1733143533626c.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
11
1
2018
08
01
Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions
133
143
EN
Arzu
Akgul
Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli, Turkey.
akgulcagla@hotmail.com
10.22130/scma.2018.61252.220
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].
Analytic functions,Univalent functions,Bi-univalent functions,Taylor-Maclaurin series,Koebe function,Starlike and convex functions,Coefficient bounds,Polylogarithm functions
https://scma.maragheh.ac.ir/article_31813.html
https://scma.maragheh.ac.ir/article_31813_4b05488564ecc7fb962eff344c90a60f.pdf