University of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801Coherent Frames1113219510.22130/scma.2018.68276.261ENAtaollahAskari HemmatDepartment of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O.Box 76169-133, Kerman, Iran.AhmadSafapourDepartment of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.0000-0002-8595-9565ZohrehYazdani 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 frameshttps://scma.maragheh.ac.ir/article_32195_afa7e7e72abfe740af573ccc4c15cbac.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801On Polar Cones and Differentiability in Reflexive Banach Spaces13233221510.22130/scma.2018.72221.284ENIldarSadeqiDepartment of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.0000-0001-5336-6186SimaHassankhaliDepartment of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.Journal Article20170926Let $X$ 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.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801Meir-Keeler Type Contraction Mappings in $c_0$-triangular Fuzzy Metric Spaces25413143610.22130/scma.2018.60715.215ENMasoomehHezarjaribiDepartment 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 $\alpha\Delta$-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.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions43632795310.22130/scma.2017.27953ENSanjibKumar DattaDepartment of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.TanmayBiswasRajbari, 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.https://scma.maragheh.ac.ir/article_27953_14efa717fdebe100e756052a42d77176.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801$G$-dual Frames in Hilbert $C^{*}$-module Spaces65793219610.22130/scma.2018.74231.310ENFatemehGhobadzadehDepartment of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.AbbasNajatiDepartment of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.0000-0001-7563-0507Journal 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.https://scma.maragheh.ac.ir/article_32196_3364381d248abfc90aba70ebe0afb964.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801Some Fixed Point Results for the Generalized $F$-suzuki Type Contractions in $b$-metric Spaces81893137910.22130/scma.2018.52976.155ENSumitChandokSchool of Mathematics, Thapar University, Patiala-147004, India.0000-0003-1928-2952HuapingHuangSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China.0000-0002-1836-2873StojanRadenovićFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.0000-0001-8254-6688Journal 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.https://scma.maragheh.ac.ir/article_31379_085d0dfa121b0af90091cb95f787a50b.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras91972370210.22130/scma.2017.23702ENFatemehGolfarshchiDepartment of Multimedia, Tabriz
Islamic Art University, Tabriz, Iran.Ali AsgharKhalilzadehDepartment of Mathematics, Sahand University of Technology, Sahand Street, Tabriz, Iran.Journal Article20160528Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $\varphi:A\rightarrow A$ 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.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801A Coupled Random Fixed Point Result With Application in Polish Spaces991132850610.22130/scma.2017.28506ENRashwan AhmedRashwanDepartment of Mathematics, Faculty of Science, Assuit University, Assuit 71516, Egypt.1234567892345678Hasanen Abuel-MagdHammadDepartment 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.https://scma.maragheh.ac.ir/article_28506_00489e0591464d632713e87b210c626a.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801The Integrating Factor Method in Banach Spaces1151323155910.22130/scma.2018.63445.240ENJosefinaAlvarezDepartment of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003, USA.CarolinaEspinoza-VillalvaDepartamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.MarthaGuzman-PartidaDepartamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.0000-0002-8807-3778Journal 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.https://scma.maragheh.ac.ir/article_31559_3d3a29c3ca9569969a1733143533626c.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580711120180801Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions1331433181310.22130/scma.2018.61252.220ENArzuAkgulDepartment 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].https://scma.maragheh.ac.ir/article_31813_4b05488564ecc7fb962eff344c90a60f.pdf