University of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801Coherent Frames1113219510.22130/scma.2018.68276.261ENAtaollah Askari HemmatDepartment of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O.Box 76169-133, Kerman, Iran.Ahmad SafapourDepartment of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.Zohreh Yazdani FardDepartment of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.Journal Article20170717Frames 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 framesUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801On Polar Cones and Differentiability in Reflexive Banach Spaces13233221510.22130/scma.2018.72221.284ENIldar SadeqiDepartment of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.Sima HassankhaliDepartment of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.Journal Article20170926Let $X$ 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 ${mathop{rm int}}(mathrm{dom} sigma_C)$.University of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801Meir-Keeler Type Contraction Mappings in $c_0$-triangular Fuzzy Metric Spaces25413143610.22130/scma.2018.60715.215ENMasoomeh HezarjaribiDepartment of Mathematics, Payame Noor University, p.o.box.19395-3697, Tehran, Iran.Journal Article20170312Proving 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions43632795310.22130/scma.2017.27953ENSanjib Kumar DattaDepartment of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.Tanmay BiswasRajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.Journal Article20160618In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801$G$-dual Frames in Hilbert $C^{*}$-module Spaces65793219610.22130/scma.2018.74231.310ENFatemeh GhobadzadehDepartment of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.Abbas NajatiDepartment of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.Journal Article20171024In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801Some Fixed Point Results for the Generalized $F$-suzuki Type Contractions in $b$-metric Spaces81893137910.22130/scma.2018.52976.155ENSumit ChandokSchool of Mathematics, Thapar University, Patiala-147004, India.Huaping HuangSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China.Stojan RadenovićFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.Journal Article20161117Compared 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras91972370210.22130/scma.2017.23702ENFatemeh GolfarshchiDepartment of Multimedia, Tabriz
Islamic Art University, Tabriz, Iran.Ali Asghar KhalilzadehDepartment of Mathematics, Sahand University of Technology, Sahand Street, Tabriz, Iran.Journal Article20160528Let $A$ 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 $A$.University of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801A Coupled Random Fixed Point Result With Application in Polish Spaces991132850610.22130/scma.2017.28506ENRashwan Ahmed RashwanDepartment of Mathematics, Faculty of Science, Assuit University, Assuit 71516, Egypt.Hasanen Abuel-Magd HammadDepartment of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.Journal Article20170201In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801The Integrating Factor Method in Banach Spaces1151323155910.22130/scma.2018.63445.240ENJosefina AlvarezDepartment of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003, USA.Carolina Espinoza-VillalvaDepartamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.Martha Guzman-PartidaDepartamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.Journal Article20170505The 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions1331433181310.22130/scma.2018.61252.220ENArzu AkgulDepartment of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli, Turkey.Journal Article20170328In 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].