Pub Date : 2020-11-01DOI: 10.22130/SCMA.2020.124021.772
M. Golmohammadi, S. Najafzadeh, M. Foroutan
In this paper, by making use of $(p , q) $-derivative operator we introduce a new subclass of meromorphically univalent functions. Precisely, we give a necessary and sufficient coefficient condition for functions in this class. Coefficient estimates, extreme points, convex linear combination, Radii of starlikeness and convexity and finally partial sum property are investigated.
{"title":"Some Properties of Certain Subclass of Meromorphic Functions Associated with $(p , q)$-derivative","authors":"M. Golmohammadi, S. Najafzadeh, M. Foroutan","doi":"10.22130/SCMA.2020.124021.772","DOIUrl":"https://doi.org/10.22130/SCMA.2020.124021.772","url":null,"abstract":"In this paper, by making use of $(p , q) $-derivative operator we introduce a new subclass of meromorphically univalent functions. Precisely, we give a necessary and sufficient coefficient condition for functions in this class. Coefficient estimates, extreme points, convex linear combination, Radii of starlikeness and convexity and finally partial sum property are investigated.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45287711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-01DOI: 10.22130/SCMA.2020.119494.733
E. Nasrabadi
Let $S$ be a (not necessarily commutative) Clifford semigroup with idempotent set $E$. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) module cohomology group of semigroup algbera $ell^1(S)$ with coefficients in $ell^infty(S)$ (and also $ell^1(S)^{(2n-1)}$ for $nin mathbb{N}$) are equal.
{"title":"First and Second Module Cohomology Groups for Non Commutative Semigroup Algebras","authors":"E. Nasrabadi","doi":"10.22130/SCMA.2020.119494.733","DOIUrl":"https://doi.org/10.22130/SCMA.2020.119494.733","url":null,"abstract":"Let $S$ be a (not necessarily commutative) Clifford semigroup with idempotent set $E$. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) module cohomology group of semigroup algbera $ell^1(S)$ with coefficients in $ell^infty(S)$ (and also $ell^1(S)^{(2n-1)}$ for $nin mathbb{N}$) are equal.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47715283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-01DOI: 10.22130/SCMA.2020.121559.748
A. Khoddami
Let $A$ be a non-zero normed vector space and let $K=overline{B_1^{(0)}}$ be the closed unit ball of $A$. Also, let $varphi$ be a non-zero element of $ A^*$ such that $Vert varphi Vertleq 1$. We first define a new norm $Vert cdot Vert_varphi$ on $C^b(K)$, that is a non-complete, non-algebraic norm and also non-equivalent to the norm $Vert cdot Vert_infty$. We next show that for $0neqpsiin A^*$ with $Vert psi Vertleq 1$, the two norms $Vert cdot Vert_varphi$ and $Vert cdot Vert_psi$ are equivalent if and only if $varphi$ and $psi$ are linearly dependent. Also by applying the norm $Vert cdot Vert_varphi $ and a new product `` $cdot$ '' on $C^b(K)$, we present the normed algebra $ left( C^{bvarphi}(K), Vert cdot Vert_varphi right)$. Finally we investigate some relations between strongly zero-product preserving maps on $C^b(K)$ and $C^{bvarphi}(K)$.
{"title":"Non-Equivalent Norms on $C^b(K)$","authors":"A. Khoddami","doi":"10.22130/SCMA.2020.121559.748","DOIUrl":"https://doi.org/10.22130/SCMA.2020.121559.748","url":null,"abstract":"Let $A$ be a non-zero normed vector space and let $K=overline{B_1^{(0)}}$ be the closed unit ball of $A$. Also, let $varphi$ be a non-zero element of $ A^*$ such that $Vert varphi Vertleq 1$. We first define a new norm $Vert cdot Vert_varphi$ on $C^b(K)$, that is a non-complete, non-algebraic norm and also non-equivalent to the norm $Vert cdot Vert_infty$. We next show that for $0neqpsiin A^*$ with $Vert psi Vertleq 1$, the two norms $Vert cdot Vert_varphi$ and $Vert cdot Vert_psi$ are equivalent if and only if $varphi$ and $psi$ are linearly dependent. Also by applying the norm $Vert cdot Vert_varphi $ and a new product `` $cdot$ '' on $C^b(K)$, we present the normed algebra $ left( C^{bvarphi}(K), Vert cdot Vert_varphi right)$. Finally we investigate some relations between strongly zero-product preserving maps on $C^b(K)$ and $C^{bvarphi}(K)$.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42703911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-01DOI: 10.22130/SCMA.2020.121797.756
Fidan Seyidova
In this work systems of sines $sin left(n+beta right)t,, , n=1,2, ldots,$ and cosines $cos left(n-beta right)t,, , n=0,1,2, ldots,$ are considered, where $beta in R-$is a real parameter. The subspace $M^{p,alpha } left(0,pi right)$ of the Morrey space $L^{p,alpha } left(0,pi right)$ in which continuous functions are dense is considered. Criterion for the completeness, minimality and basicity of these systems with respect to the parameter $beta $ in the subspace $M^{p,alpha } left(0,pi right)$, $1
{"title":"On the Basicity of Systems of Sines and Cosines with a Linear Phase in Morrey-Type Spaces","authors":"Fidan Seyidova","doi":"10.22130/SCMA.2020.121797.756","DOIUrl":"https://doi.org/10.22130/SCMA.2020.121797.756","url":null,"abstract":"In this work systems of sines $sin left(n+beta right)t,, , n=1,2, ldots,$ and cosines $cos left(n-beta right)t,, , n=0,1,2, ldots,$ are considered, where $beta in R-$is a real parameter. The subspace $M^{p,alpha } left(0,pi right)$ of the Morrey space $L^{p,alpha } left(0,pi right)$ in which continuous functions are dense is considered. Criterion for the completeness, minimality and basicity of these systems with respect to the parameter $beta $ in the subspace $M^{p,alpha } left(0,pi right)$, $1","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48468828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-01DOI: 10.22130/SCMA.2020.123056.766
Habib Shakoory, R. Ahmadi, N. Behzadi, S. Nami
In this manuscript, we study the relation between K-fusion frame and its local components which leads to the definition of a $C$-controlled $K$-fusion frames, also we extend a theory based on K-fusion frames on Hilbert spaces, which prepares exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we define the analysis, synthesis and frame operator for $C$-controlled $K$-fusion frames, which even yield a reconstruction formula. Also, we define dual of $C$-controlled $K$-fusion frames and study some basic properties and perturbation of them.
{"title":"A Note on Some Results for $C$-controlled $K$-Fusion Frames in Hilbert Spaces","authors":"Habib Shakoory, R. Ahmadi, N. Behzadi, S. Nami","doi":"10.22130/SCMA.2020.123056.766","DOIUrl":"https://doi.org/10.22130/SCMA.2020.123056.766","url":null,"abstract":"In this manuscript, we study the relation between K-fusion frame and its local components which leads to the definition of a $C$-controlled $K$-fusion frames, also we extend a theory based on K-fusion frames on Hilbert spaces, which prepares exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we define the analysis, synthesis and frame operator for $C$-controlled $K$-fusion frames, which even yield a reconstruction formula. Also, we define dual of $C$-controlled $K$-fusion frames and study some basic properties and perturbation of them.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46429442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.22130/SCMA.2019.111716.644
Sinan Ercan
The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of the space $fleft( lambda _{r}right) $. Finally, we give the characterization of some matrix classes.
{"title":"On the Spaces of $lambda _{r}$-almost Convergent and $lambda _{r}$-almost Bounded Sequences","authors":"Sinan Ercan","doi":"10.22130/SCMA.2019.111716.644","DOIUrl":"https://doi.org/10.22130/SCMA.2019.111716.644","url":null,"abstract":"The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of the space $fleft( lambda _{r}right) $. Finally, we give the characterization of some matrix classes.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49454496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.22130/SCMA.2019.113393.665
Nasrin Ebrahimi Hoseinzadeh, A. Bodaghi, M. Mardanbeigi
The aim of this paper is to introduce $n$-variables mappings which are cubic in each variable and to apply a fixed point theorem for the Hyers-Ulam stability of such mapping in non-Archimedean normed spaces. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes are presented.
{"title":"Almost Multi-Cubic Mappings and a Fixed Point Application","authors":"Nasrin Ebrahimi Hoseinzadeh, A. Bodaghi, M. Mardanbeigi","doi":"10.22130/SCMA.2019.113393.665","DOIUrl":"https://doi.org/10.22130/SCMA.2019.113393.665","url":null,"abstract":"The aim of this paper is to introduce $n$-variables mappings which are cubic in each variable and to apply a fixed point theorem for the Hyers-Ulam stability of such mapping in non-Archimedean normed spaces. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes are presented.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41860452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.22130/SCMA.2019.116000.696
S. Barootkoob
In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity and also strong Arens irregularity. These results may help us to prove some previous problems related to strong Arens irregularity more easier than old. These include some results proved by Neufang in ~cite{neu1} and ~cite{neu}. Some applications to certain bilinear mappings on convolution algebras, on a locally compact group, are also included. Finally, some solutions related to the Ghahramani-Lau conjecture is raised.
{"title":"$n$-factorization Property of Bilinear Mappings","authors":"S. Barootkoob","doi":"10.22130/SCMA.2019.116000.696","DOIUrl":"https://doi.org/10.22130/SCMA.2019.116000.696","url":null,"abstract":"In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity and also strong Arens irregularity. These results may help us to prove some previous problems related to strong Arens irregularity more easier than old. These include some results proved by Neufang in ~cite{neu1} and ~cite{neu}. Some applications to certain bilinear mappings on convolution algebras, on a locally compact group, are also included. Finally, some solutions related to the Ghahramani-Lau conjecture is raised.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43504069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.22130/SCMA.2019.99206.533
Tesfalem Hadush Meche, H. Zegeye
In this article, we introduced an iterative scheme for finding a common element of the set of fixed points of a multi-valued hemicontractive-type mapping, the set of common solutions of a finite family of split equilibrium problems and the set of common solutions of a finite family of variational inequality problems in real Hilbert spaces. Moreover, the sequence generated by the proposed algorithm is proved to be strongly convergent to a common solution of these three problems under mild conditions on parameters. Our results improve and generalize many well-known recent results existing in the literature in this field of research.
{"title":"On fixed point results for hemicontractive-type multi-valued mapping, finite families of split equilibrium and variational inequality problems","authors":"Tesfalem Hadush Meche, H. Zegeye","doi":"10.22130/SCMA.2019.99206.533","DOIUrl":"https://doi.org/10.22130/SCMA.2019.99206.533","url":null,"abstract":"In this article, we introduced an iterative scheme for finding a common element of the set of fixed points of a multi-valued hemicontractive-type mapping, the set of common solutions of a finite family of split equilibrium problems and the set of common solutions of a finite family of variational inequality problems in real Hilbert spaces. Moreover, the sequence generated by the proposed algorithm is proved to be strongly convergent to a common solution of these three problems under mild conditions on parameters. Our results improve and generalize many well-known recent results existing in the literature in this field of research.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45564178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.22130/SCMA.2019.100548.540
A. Ghaffari, S. Javadi, Ebrahim Tamimi
Let $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such as Segal algebras and $L^1$-algebras are responsive to this concept. It is also shown that $Wap(A)$ has a left invariant $varphi$-mean if and only if there exists a bounded net $left{a_alpharight}_{alphain I}$ in $left{ain A; varphi(a)=1right}$ such that $|aa_alpha-varphi(a)a_alpha|_{Wap(A)}to0$ uniformly for all $a$ in weakly compact subsets of $A$. Other results in this direction are also obtained.
设$left{a_alpharight}_{alphain I}$是Banach代数$ a $上的一个有界网，$varphi$是$ a $上的一个非零乘法线性泛函。本文讨论了当$|aa_alpha-varphi(a)a_alpha|趋近于0$时，对于$a$的弱紧子集中的所有$a$的一致问题。我们证明了与局部紧群相关的Banach代数如Segal代数和$L^1$-代数是响应这个概念的。还证明了$Wap(A)$具有左不变量$varphi$-mean当且仅当$left{ain A中存在有界网$left{a_alpharight}_{alphain I}$;varphi(a)=1right}$使得$|aa_alpha-varphi(a)a_alpha|_{Wap(a)}to0$对于所有$a$弱紧集合中的$a$一致。在这个方向上也得到了其他结果。
{"title":"Uniform Convergence to a Left Invariance on Weakly Compact Subsets","authors":"A. Ghaffari, S. Javadi, Ebrahim Tamimi","doi":"10.22130/SCMA.2019.100548.540","DOIUrl":"https://doi.org/10.22130/SCMA.2019.100548.540","url":null,"abstract":"Let $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such as Segal algebras and $L^1$-algebras are responsive to this concept. It is also shown that $Wap(A)$ has a left invariant $varphi$-mean if and only if there exists a bounded net $left{a_alpharight}_{alphain I}$ in $left{ain A; varphi(a)=1right}$ such that $|aa_alpha-varphi(a)a_alpha|_{Wap(A)}to0$ uniformly for all $a$ in weakly compact subsets of $A$. Other results in this direction are also obtained.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45379912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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