University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions1142424010.22130/scma.2018.24240ENMaliheh MayghaniDepartment of Mathematics, Payame Noor University, P. O. Box: 19359-3697, Tehran, Iran.Davood AlimohammadiDepartment of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran.Journal Article20161127We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we prove that every unital endomorphism of real Lipschitz algebras of complex-valued functions on compact metric spaces with Lipschitz involutions is a composition operator. Finally, we study some properties of quasicompact and Riesz unital endomorphisms of these algebras.University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101On an atomic decomposition in Banach spaces15322298410.22130/scma.2018.22984ENTelman GasymovDepartment of Non-harmonic analysis,Institute of Mathematics and
Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.Chingiz HashimovGanja State University, Ganja, Azerbaijan.Journal Article20160607An atomic decomposition is considered in Banach space. A method for constructing an atomic decomposition of Banach space, starting with atomic decomposition of subspaces is presented. Some relations between them are established. The proposed method is used in the study of the frame properties of systems of eigenfunctions and associated functions of discontinuous differential operators.University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101Density near zero33432368210.22130/scma.2018.23682ENElham BayatmaneshDepartment of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.Mohammad Akbari TootkaboniDepartment of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.Journal Article20160924Let $S$ be a dense subsemigroup of $(0,+infty)$. In this paper, we state definition of thick near zero, and also we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman and Leader in [6]. We define density near zero for subsets of $S$ by a collection of nonempty finite subsets of $S$ and we investigate the conditions under these concepts.University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101On the stability of the Pexiderized cubic functional equation in multi-normed spaces45832475510.22130/scma.2018.24755ENMahdi NazarianpoorDepartment of Mathematics and Computer
Sciences, Hakim Sabzevari University, Sabzevar, Iran.Ghadir SadeghiDepartment of Mathematics and Computer
Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.Journal Article20161022In this paper, we investigate the Hyers-Ulam stability of the orthogonally cubic equation and Pexiderized cubic equation <br />[<br />f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+frac{2}{k}g(kx)-2g(x),<br />]<br />in multi-normed spaces by the direct method and the fixed point method. Moreover, we prove the Hyers-Ulam stability of the $2$-variables cubic equation <br />[<br /> f(2x+y,2z+t)+f(2x-y,2z-t) =2f(x+y,z+t) +2f(x-y,z-t)+12f(x,z),<br />]<br />and orthogonally cubic type and $k$-cubic equation in multi-normed spaces. A counter example for non stability of the cubic equation is also discussed.University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101Non-Archimedean fuzzy metric spaces and Best proximity point theorems851122462710.22130/scma.2018.24627ENMohadeseh PaknazarDepartment of Mathematics, Farhangian University, Iran.0000-0001-9327-7911Journal Article20161023In this paper, we introduce some new classes of proximal contraction mappings and establish best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the usability of the obtained results.University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101On the cyclic Homology of multiplier Hopf algebras1131282364510.22130/scma.2018.23645ENGhorbanali HaghighatdoostDepartment of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.Hami Abbasi MakraniDepartment of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.Rasoul MahjoubiDepartment of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.Journal Article20160306In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a paracyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ and then prove the existence of a cyclic structure associated to this triple.University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101Frames in super Hilbert modules1291422384710.22130/scma.2018.23847ENMehdi Rashidi-KouchiYoung Researchers and Elite Club
Kahnooj Branch, Islamic Azad University, Kerman, Iran.Journal Article20161017In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101A cone theoretic Krein-Milman theorem in semitopological cones1431502475610.22130/scma.2018.24756ENAli HassanzadehDepartment of Mathematics, Sahand University of Technology, Tabriz, Iran.Ildar SadeqiDepartment of Mathematics, Sahand University of Technology, Tabriz, Iran.Journal Article20161226In this paper, a Krein-Milman type theorem in $T_0$ semitopological cone is proved, in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.