University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules1183496810.22130/scma.2018.77908.356ENMohammadMahmoudiehSchool of Mathematics and computer Science, Damghan University, Damghan, Iran.HessamHosseinnezhadSchool of Mathematics and computer Science, Damghan University, Damghan, Iran.GholamrezaAbbaspour TabadkanSchool of Mathematics and computer Science, Damghan University, Damghan, Iran.Journal Article20171223In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective operator is replaced by unitary and invertible operators, respectively. Moreover, we show that new multi-frames (resp. multi-Riesz bases) can be obtained as linear combinations of known ones using coefficients which are operators in a certain class.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701A Generalization of the Meir-Keeler Condensing Operators and its Application to Solvability of a System of Nonlinear Functional Integral Equations of Volterra Type19353495410.22130/scma.2018.74869.322ENShahramBanaeiDepartment of Mathematics, Bonab Branch, Islamic Azad University, Bonab, Iran.Mohammad BagherGhaemiDepartment of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.Journal Article20171109In this paper, we generalize the Meir-Keeler condensing operators via a concept of the class of operators $ O (f;.)$, that was given by Altun and Turkoglu [4], and apply this extension to obtain some tripled fixed point theorems. As an application of this extension, we analyze the existence of solution for a system of nonlinear functional integral equations of Volterra type. Finally, we present an example to show the effectiveness of our results. We use the technique of measure of noncompactness to obtain our results.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Controlled Continuous $G$-Frames and Their Multipliers in Hilbert Spaces37483496310.22130/scma.2019.68582.264ENYahyaAlizadehDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.Mohammad RezaAbdollahpourDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.Journal Article20170722In this paper, we introduce $(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frames is a $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel multiplier is a p-Schatten class operator.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem49633496410.22130/scma.2018.74791.321ENZahraKalateh BojdiDepartment of Mathematics, Faculty of Science and New Technologies, Graduate University of Advanced Technology, Kerman, Iran.AtaollahAskari HemmatDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman,
Kerman, Iran.AliTavakoliMathematics department, University of Mazandaran, Babolsar, Iran.Journal Article20171104In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function and a sevenfold 3D wavelet and all of our computations are based on this new set to approximate in 3D spatial. Moreover, approximation in time domain is based on finite difference method. By substitution in the 3D DPL model, the differential equation converts to a linear system of equations and related system is solved directly. We use the Lax-Richtmyer theorem to investigate the consistency, stability and convergence analysis of our method. Numerical results are presented and compared with the analytical solution to show the efficiency of the method.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Theory of Hybrid Fractional Differential Equations with Complex Order65763496710.22130/scma.2018.72907.295ENDevarajVivekDepartment of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.OmidBaghaniDepartment of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.KuppusamyKanagarajanDepartment of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.Journal Article20171003We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the existence of mild solutions of initial value problems for hybrid fractional differential equations. Finally, an application to solve one-variable linear fractional Schr"odinger equation with complex order is given.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701$sigma$-Connes Amenability and Pseudo-(Connes) Amenability of Beurling Algebras77893496910.22130/scma.2018.73939.308ENZahraHasanzadehDepartment of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.AminMahmoodiDepartment of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.Journal Article20171019In this paper, pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Convergence of an Iterative Scheme for Multifunctions on Fuzzy Metric Spaces911063507010.22130/scma.2018.72350.288ENMohammad EsmaelSameiDepartment of Mathematics, Faculty of Science, Bu-Ali Sina University, 6517838695, Hamedan, Iran.0000-0002-5450-3127Journal Article20170922Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In 2011, Aleomraninejad, et. al. generalized some of their results to Suzuki-type multifunctions. The study of iterative schemes for various classes of contractive and nonexpansive mappings is a central topic in fixed point theory. The importance of Banach contraction principle is that it also gives the convergence of an iterative scheme to a unique fixed point. In this paper, we consider $(X, M, *)$ to be fuzzy metric spaces in Park's sense and we show our results for fixed points of contractive and nonexpansive multifunctions on Hausdorff fuzzy metric space.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Bounded Approximate Character Amenability of Banach Algebras1071183543510.22130/scma.2018.79315.372ENHasanPourmahmood AghababaDepartment of Mathematics, University of Tabriz, Tabriz, Iran.FouroghKhedriDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.Mohammad HosseinSattariDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.Journal Article20180115The bounded approximate version of $varphi$-amenability and character amenability are introduced and studied. These new notions are characterized in several different ways, and some hereditary properties of them are established. The general theory for these concepts is also developed. Moreover, some examples are given to show that these notions are different from the others. Finally, bounded approximate character amenability of some Banach algebras related to locally compact groups are investigated.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Generalized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces1191333572410.22130/scma.2018.78754.365ENKobraEsmaeiliFaculty of Engineering, Ardakan University, P.O. Box 184, Ardakan, Iran.Journal Article20180105Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|<infty.$ Endowed with the norm <br />begin{align*}<br />left|f right|_{mathcal{W}_mu ^{(n)}}=sum_{j=0}^{n-1}left|f^{(j)}(0)right|+sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|,<br />end{align*}<br />the $n$'th weighted type space is a Banach space. In this paper, we characterize the boundedness of generalized weighted composition operators $mathcal{D}_{varphi ,u}^m$ from logarithmic Bloch type spaces $mathcal{B}_{{{log }^beta }}^alpha $ to $n$'th weighted type spaces $ mathcal{W}_mu ^{(n)} $, where $u$ and $varphi$ are analytic functions on $mathbb{D}$ and $varphi(mathbb{D})subseteqmathbb{D}$. We also provide an estimation for the essential norm of these operators.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules1351463572610.22130/scma.2018.81624.396ENMortezaMirzaee AzandaryaniDepartment of Mathematics, University of Qom, Qom, Iran.Journal Article20180216In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and fusion frames to Hilbert $C^ast-$modules, where $Q$ is an adjointable operator, and obtain some properties of this kind of approximate duals.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Primitive Ideal Space of Ultragraph $C^*$-algebras1471583572910.22130/scma.2018.82725.404ENMostafaImanfarFaculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.AbdolrasoulPourabbasFaculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.HosseinLarkiDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Iran.Journal Article20180306In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$ associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $ C^* $-algebra $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the Hong and Szyma$ acute{ mathrm { n } } $ski's description of the primitive ideal space of a graph $ C ^ * $-algebra by a simpler method.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Proximity Point Properties for Admitting Center Maps1591673572710.22130/scma.2018.79127.368ENMohammad HoseinLabbaf GhasemiDepartment of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 88186-34141, Iran.Mohammad RezaHaddadiFaculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.NohaEftekhariDepartment of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 88186-34141, Iran.0000-0002-8159-1652Journal Article20180119In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we show that in some conditions, the set of all best proximity points is nonempty and compact.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Some Properties of Continuous $K$-frames in Hilbert Spaces1691873596410.22130/scma.2018.85866.432ENGholamrezaRahimlouDepartment of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.RezaAhmadiInstitute of Fundamental Sciences, University of Tabriz, Tabriz, Iran.Mohammad AliJafarizadehFaculty of Physic, University of Tabriz,
Tabriz, Iran.SusanNamiFaculty of Physic, University of Tabriz,
Tabriz, Iran.Journal Article20180509The theory of continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory. The $K$-frames were introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of $K$-frames, there are many differences between $K$-frames and standard frames. $K$-frames, which are a generalization of frames, allow us in a stable way, to reconstruct elements from the range of a bounded linear operator in a Hilbert space. In this paper, we get some new results on the continuous $K$-frames or briefly c$K$-frames, namely some operators preserving and some identities for c$K$-frames. Also, the stability of these frames are discussed.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701A Proposed Preference Index For Ranking Fuzzy Numbers Based On $alpha$-Optimistic Values1892013573410.22130/scma.2018.73477.303ENMehdiShamsDepartment of Statistics, School of Mathematics, University of Kashan, Kashan,Iran.0000-0002-9645-9195GholamrezaHesamianDepartment of Mathematical Sciences, Payame Noor University, Tehran, Iran.Journal Article20171011In this paper, we propose a novel method for ranking a set of fuzzy numbers. In this method a preference index is proposed based on $alpha$-optimistic values of a fuzzy number. We propose a new ranking method by adopting a level of credit in the ordering procedure. Then, we investigate some desirable properties of the proposed ranking method.University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Topological Centers and Factorization of Certain Module Actions2032153572310.22130/scma.2018.76242.344ENSedighehBarootkoobDepartment of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran.0000-0003-1489-0975Journal Article20171126Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule with the left and right module actions $pi_ell: Atimes Xrightarrow X$ and $pi_r: Xtimes Arightarrow X$, respectively. In this paper, we study the topological centers of the left module action $pi_{ell_n}: Atimes X^{(n)}rightarrow X^{(n)}$ and the right module action $pi_{r_n}:X^{(n)}times Arightarrow X^{(n)}$, which inherit from the module actions $pi_ell$ and $pi_r$, and also the topological centers of their adjoints, from the factorization property point of view, and then, we investigate conditions under which these bilinear maps are Arens regular or strongly Arens irregular.