Pub Date : 2019-07-01DOI: 10.22130/SCMA.2018.78754.365
K. Esmaeili
Let $ 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 $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|
设$mathcal｛H｝（mathbb｛D｝）$表示开单位圆盘$mathbb{D｝$上解析函数的空间。对于权重$mu$和非负整数$n$，第$n$个加权类型空间$mathcal{W}_mu^｛（n）｝$是所有$fin-mathcal｛H｝（mathbb｛D｝赋以范数开始{align*}left |f right |_{mathcal{W}_mu^｛（n）｝｝=sum_｛j=0｝^{n-1}left|f^{（j）}（0）右|+sup_｛zin-mathbb｛D｝｝mu（z）左|f^{（n）}（z）右|，end｛align*｝第$n$个加权类型空间是Banach空间。在本文中，我们刻画了广义加权复合算子$mathcal的有界性{D}_｛varphi，u｝^m$来自对数Bloch类型空间$mathcal{B}_｛｛log｝^beta｝｝^alpha$到第$n$个加权类型空间$mathcal{W}_mu^｛（n）｝$，其中$u$和$varphi$是$mathbb｛D｝$和$varphi（mathbb{D｝）substeqmathbb｛D}$上的分析函数。我们还对这些算子的本质范数进行了估计。
{"title":"Generalized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces","authors":"K. Esmaeili","doi":"10.22130/SCMA.2018.78754.365","DOIUrl":"https://doi.org/10.22130/SCMA.2018.78754.365","url":null,"abstract":"Let $ 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 begin{align*}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|,end{align*}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.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"119-133"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49102437","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 : 2019-07-01DOI: 10.22130/SCMA.2018.74791.321
Z. K. Bojdi, A. A. Hemmat, A. Tavakoli
In 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.
{"title":"Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem","authors":"Z. K. Bojdi, A. A. Hemmat, A. Tavakoli","doi":"10.22130/SCMA.2018.74791.321","DOIUrl":"https://doi.org/10.22130/SCMA.2018.74791.321","url":null,"abstract":"In 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.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"49-63"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48912417","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 : 2019-07-01DOI: 10.22130/SCMA.2018.79315.372
H. P. Aghababa, F. Khedri, M. Sattari
The 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.
{"title":"Bounded Approximate Character Amenability of Banach Algebras","authors":"H. P. Aghababa, F. Khedri, M. Sattari","doi":"10.22130/SCMA.2018.79315.372","DOIUrl":"https://doi.org/10.22130/SCMA.2018.79315.372","url":null,"abstract":"The 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.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"107-118"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48345219","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 : 2019-07-01DOI: 10.22130/SCMA.2018.85866.432
Gholamreza Rahimlou, R. Ahmadi, M. Jafarizadeh, S. Nami
The 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.
{"title":"Some Properties of Continuous $K$-frames in Hilbert Spaces","authors":"Gholamreza Rahimlou, R. Ahmadi, M. Jafarizadeh, S. Nami","doi":"10.22130/SCMA.2018.85866.432","DOIUrl":"https://doi.org/10.22130/SCMA.2018.85866.432","url":null,"abstract":"The 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.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"169-187"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45452445","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 : 2019-07-01DOI: 10.22130/SCMA.2018.81624.396
M. M. Azandaryani
In 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.
{"title":"Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules","authors":"M. M. Azandaryani","doi":"10.22130/SCMA.2018.81624.396","DOIUrl":"https://doi.org/10.22130/SCMA.2018.81624.396","url":null,"abstract":"In 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.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"135-146"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44251578","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 : 2019-07-01DOI: 10.22130/SCMA.2018.82725.404
M. Imanfar, A. Pourabbas, H. Larki
In 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 ^ * $-algebra by a simpler method.
本文描述了与超图$mathcal{G}$相关联的$C^*$-代数$C^*(mathcal G)$的原始理想空间。研究了不含非零集投影的商超图$C^* $-代数$C^*左(数学G/(H,S)右)$的闭理想的结构，并刻画了所有的非规不变本原理想。我们的结果用一种更简单的方法推广了Hong和Szyma$ acute{maththrm {n}} $ski关于图$ C ^ * $-代数的原始理想空间的描述。
{"title":"Primitive Ideal Space of Ultragraph $C^*$-algebras","authors":"M. Imanfar, A. Pourabbas, H. Larki","doi":"10.22130/SCMA.2018.82725.404","DOIUrl":"https://doi.org/10.22130/SCMA.2018.82725.404","url":null,"abstract":"In 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.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"147-158"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43190244","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 : 2019-07-01DOI: 10.22130/SCMA.2018.74869.322
Shahram Banaei, M. Ghaemi
In this paper, we generalize the Meir-Keeler condensing operators via a concept of the class of operators $ O (f;.)$, that was given by Altun and Turkoglu [4], and apply this extension to obtain some tripled fixed point theorems. As an application of this extension, we analyze the existence of solution for a system of nonlinear functional integral equations of Volterra type. Finally, we present an example to show the effectiveness of our results. We use the technique of measure of noncompactness to obtain our results.
本文利用Altun和Turkoglu[4]给出的算子类$ O (f;)$的概念，推广了Meir-Keeler压缩算子，并应用这一推广得到了一些三倍不动点定理。作为推广的一个应用，我们分析了一类非线性泛函积分方程组Volterra型解的存在性。最后，给出了一个算例，说明了结果的有效性。我们使用非紧性度量技术来得到我们的结果。
{"title":"A Generalization of the Meir-Keeler Condensing Operators and its Application to Solvability of a System of Nonlinear Functional Integral Equations of Volterra Type","authors":"Shahram Banaei, M. Ghaemi","doi":"10.22130/SCMA.2018.74869.322","DOIUrl":"https://doi.org/10.22130/SCMA.2018.74869.322","url":null,"abstract":"In 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.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"19-35"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48480106","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 : 2019-07-01DOI: 10.22130/SCMA.2018.73477.303
M. Shams, G. Hesamian
In 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.
{"title":"A Proposed Preference Index For Ranking Fuzzy Numbers Based On $alpha$-Optimistic Values","authors":"M. Shams, G. Hesamian","doi":"10.22130/SCMA.2018.73477.303","DOIUrl":"https://doi.org/10.22130/SCMA.2018.73477.303","url":null,"abstract":"In 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.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"189-201"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49023328","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 : 2019-07-01DOI: 10.22130/SCMA.2018.72350.288
M. Samei
Recently, 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.
{"title":"Convergence of an Iterative Scheme for Multifunctions on Fuzzy Metric Spaces","authors":"M. Samei","doi":"10.22130/SCMA.2018.72350.288","DOIUrl":"https://doi.org/10.22130/SCMA.2018.72350.288","url":null,"abstract":"Recently, 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.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"91-106"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47912028","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 : 2019-07-01DOI: 10.22130/SCMA.2018.79127.368
M. Ghasemi, M. Haddadi, N. Eftekhari
In 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.
{"title":"Proximity Point Properties for Admitting Center Maps","authors":"M. Ghasemi, M. Haddadi, N. Eftekhari","doi":"10.22130/SCMA.2018.79127.368","DOIUrl":"https://doi.org/10.22130/SCMA.2018.79127.368","url":null,"abstract":"In 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.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"159-167"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43230679","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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