University of MaraghehSahand Communications in Mathematical Analysis2322-580708120171001$G$-Frames for operators in Hilbert spaces1212364610.22130/scma.2017.23646ENBahramDastourianDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.MohammadJanfadaDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.0000-0002-3016-4028Journal Article20160625$K$-frames as a generalization of frames were introduced by L. G\u{a}vru\c{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new generalization of $K$-frames. After proving some characterizations of generalized $K$-frames, new results are investigated and some new perturbation results are established. Finally, we give several characterizations of $K$-duals.https://scma.maragheh.ac.ir/article_23646_5b6f187d7a7e622a7634cf56284bc2c6.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580708120171001Generalized Ritt type and generalized Ritt weak type connected growth properties of entire functions represented by vector valued Dirichlet series23322263610.22130/scma.2017.22636ENSanjib KumarDattaDepartment 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.Jinarul HaqueShaikhDepartment of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.Journal Article20151107In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.https://scma.maragheh.ac.ir/article_22636_d44441b3c78ee5e56778a0617e77ab53.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580708120171001Second dual space of little $\alpha$-Lipschitz vector-valued operator algebras33412307210.22130/scma.2017.23072ENAbbasaliShokriDepartment of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.Journal Article20160312Let $(X,d)$ be an infinite compact metric space, let $(B,\parallel . \parallel)$ be a unital Banach space, and take $\alpha \in (0,1).$ In this work, at first we define the big and little $\alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $\alpha$-lipschitz $B$-valued operator algebra, $lip_{\alpha}(X,B)$. Then we characterize its second dual space.https://scma.maragheh.ac.ir/article_23072_37fba52745f4bc2b7c6107415e1dffc2.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580708120171001Generated topology on infinite sets by ultrafilters43532333710.22130/scma.2017.23337ENAlirezaBagheri SalecDepartment of Mathematics, Faculty of Science, University of Qom, P.O.Box 3716146611, Qom, Iran.Journal Article20161023Let $X$ be an infinite set, equipped with a topology $\tau$. In this paper we studied the relationship between $\tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.https://scma.maragheh.ac.ir/article_23337_6c78346b95a2ee9f22a0f2d5078a421e.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580708120171001Contra $\beta^{*}$-continuous and almost contra $\beta^{*}$-continuous functions55712204510.22130/scma.2017.22045ENAppachiVadivelDepartment of Mathematics, Annamalai University, Annamalai Nagar-608 002, Tamil Nadu, India.0000-0001-5970-035XRadhakrishnanRameshDepartment of Mathematics, Pope John Paul II College of Education, Reddiar Palayam, Puducherry-605010, India.DuraisamySivakumarDepartment of Mathematics (DDE), Annamalai University, Annamalai Nagar-608 002, Tamil Nadu, India.Journal Article20160305The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $\beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $\beta^{*}$-continuous and almost contra $\beta^{*}$-continuous functions as a new generalization of contra continuity.https://scma.maragheh.ac.ir/article_22045_9b9885af1b47833c61470ac4706d0a25.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580708120171001Stability of additive functional equation on discrete quantum semigroups73812285210.22130/scma.2017.22852ENMaysamMaysami SadrDepartment of Mathematics, Institute for Advanced Studies in Basic Sciences, P.O.Box 45195-1159, Zanjan 45137-66731, Iran.Journal Article20160918We construct a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result generalizes a famous and old result due to Forti on the Hyers-Ulam stability of additive functional equations on amenable classical discrete semigroups.https://scma.maragheh.ac.ir/article_22852_a21e351c5081462f3ee9b1f99cdd027a.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580708120171001Compare and contrast between duals of fusion and discrete frames83962241210.22130/scma.2017.22412ENElnazOsgooeiDepartment of Sciences, Urmia University of Technology, P.O.Box 419-57155, Urmia, Iran.Ali AkbarArefijammalDepartment of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.Box 397, Sabzevar, Iran.0000-0003-2153-352XJournal Article20160629Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion frames with their associated discrete frames.https://scma.maragheh.ac.ir/article_22412_6e582d16caaf2352781eab207dfc817c.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580708120171001Subspace-diskcyclic sequences of linear operators971062385010.22130/scma.2017.23850ENMohammad RezaAzimiDepartment of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh, Iran.0000-0002-7337-1617Journal Article20160924A sequence $\{T_n\}_{n=1}^{\infty}$ of bounded linear operators on a separable infinite dimensional Hilbert space<br /> $\mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $M\subseteq \mathcal{H},$ if there exists a vector $x\in \mathcal{H}$ such that the disk-scaled orbit $\{\alpha T_n x: n\in \mathbb{N}, \alpha \in\mathbb{C}, | \alpha | \leq 1\}\cap M$ is dense in $M$. The goal of this paper is the studying of subspace diskcyclic sequence of operators like as the well known results in a single operator case. In the first section of this paper, we study some conditions that imply the diskcyclicity of $\{T_n\}_{n=1}^{\infty}$. In the second section, we survey some conditions and subspace-diskcyclicity criterion (analogue the results obtained by some authors in \cite{MR1111569, MR2261697, MR2720700}) which are sufficient for the sequence $\{T_n\}_{n=1}^{\infty}$ to be subspace-diskcyclic(subspace-hypercyclic).https://scma.maragheh.ac.ir/article_23850_39a0664f6ddf12b1b192462ffddd7aaf.pdf