Pub Date : 2020-01-01DOI: 10.22130/SCMA.2018.90101.472
Azam Yousefzadeheyni, M. R. Abdollahpour
In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Gamma_w V in Bleft(H,K_wright): win Omega}$ is again a continuous $g$-frame. Moreover, we obtain some sufficient conditions under which the finite sum of continuous $g$-frames are stable under small perturbations.
本文给出了连续$g$-系的有限和再次为连续$g$-系的若干条件。我们给出了连续的$g$-帧$Lambda=left{Lambda_w in blleft (H,K_wright): win Omegaright}$和$Gamma=left{Gamma_w in blleft (H,K_wright): win Omegaright}$以及$H$上的算子$U$和$V$的充分必要条件，使得$Lambda U+Gamma V={Lambda_w U+Gamma_w V in blleft (H,K_wright): win Omega}$又是一个连续的$g$-帧。此外，我们还得到了连续$g$-框架有限和在小扰动下稳定的几个充分条件。
{"title":"On Sum and Stability of Continuous $G$-Frames","authors":"Azam Yousefzadeheyni, M. R. Abdollahpour","doi":"10.22130/SCMA.2018.90101.472","DOIUrl":"https://doi.org/10.22130/SCMA.2018.90101.472","url":null,"abstract":"In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Gamma_w V in Bleft(H,K_wright): win Omega}$ is again a continuous $g$-frame. Moreover, we obtain some sufficient conditions under which the finite sum of continuous $g$-frames are stable under small perturbations.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"6 1","pages":"157-169"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68213633","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 : 2020-01-01DOI: 10.22130/SCMA.2019.101527.551
M. Hassanloo
Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.
{"title":"Estimates of Norm and Essential norm of Differences of Differentiation Composition Operators on Weighted Bloch Spaces","authors":"M. Hassanloo","doi":"10.22130/SCMA.2019.101527.551","DOIUrl":"https://doi.org/10.22130/SCMA.2019.101527.551","url":null,"abstract":"Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"109-124"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68213654","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 : 2020-01-01DOI: 10.22130/SCMA.2018.87694.451
P. Kaskasem, Aekarach Janchada, C. Klin-eam
In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation[ fleft( sqrt[3]{ax^3 + by^3}right)=af(x) + bf(y),] where $a,b in mathbb{R}_+$ are fixed positive real numbers, by using direct method in quasi-$beta$-Banach spaces. Moreover, we use subadditive functions to investigate stability of the generalized radical cubic functional equations in $(beta,p)$-Banach spaces.
{"title":"On Approximate Solutions of the Generalized Radical Cubic Functional Equation in Quasi-$beta$-Banach Spaces","authors":"P. Kaskasem, Aekarach Janchada, C. Klin-eam","doi":"10.22130/SCMA.2018.87694.451","DOIUrl":"https://doi.org/10.22130/SCMA.2018.87694.451","url":null,"abstract":"In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation[ fleft( sqrt[3]{ax^3 + by^3}right)=af(x) + bf(y),] where $a,b in mathbb{R}_+$ are fixed positive real numbers, by using direct method in quasi-$beta$-Banach spaces. Moreover, we use subadditive functions to investigate stability of the generalized radical cubic functional equations in $(beta,p)$-Banach spaces.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"69-90"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68213222","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 : 2019-12-21DOI: 10.22130/SCMA.2018.94775.506
R. Mikić, J. Pečarić
By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.
{"title":"Inequalities of Ando's Type for $n$-convex Functions","authors":"R. Mikić, J. Pečarić","doi":"10.22130/SCMA.2018.94775.506","DOIUrl":"https://doi.org/10.22130/SCMA.2018.94775.506","url":null,"abstract":"By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"139-159"},"PeriodicalIF":0.0,"publicationDate":"2019-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46681842","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 : 2019-12-18DOI: 10.22130/SCMA.2018.77951.362
Hamideh Mohammadzadehkan, A. Ebadian, K. Azar
In this paper, we discuss some properties of joint spectral {radius(jsr)} and generalized spectral radius(gsr) for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*left(Sigmaright)= hat{r}left(Sigmaright)$, but for a bounded set of upper triangular matrices with entries in a Banach algebra($Sigma$), $r_*left(Sigmaright)neqhat{r}left(Sigmaright)$. We investigate when the set is defective or not and equivalent properties for having a norm equal to jsr, too.
{"title":"Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra","authors":"Hamideh Mohammadzadehkan, A. Ebadian, K. Azar","doi":"10.22130/SCMA.2018.77951.362","DOIUrl":"https://doi.org/10.22130/SCMA.2018.77951.362","url":null,"abstract":"In this paper, we discuss some properties of joint spectral {radius(jsr)} and generalized spectral radius(gsr) for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*left(Sigmaright)= hat{r}left(Sigmaright)$, but for a bounded set of upper triangular matrices with entries in a Banach algebra($Sigma$), $r_*left(Sigmaright)neqhat{r}left(Sigmaright)$. We investigate when the set is defective or not and equivalent properties for having a norm equal to jsr, too.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"175-188"},"PeriodicalIF":0.0,"publicationDate":"2019-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44842071","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 : 2019-12-17DOI: 10.22130/SCMA.2018.88329.461
Z. Azimi, G. Aghamollaei
In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied. Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of values of basic A-factor block circulant matrices are investigated.
{"title":"Some Results on the Field of Values of Matrix Polynomials","authors":"Z. Azimi, G. Aghamollaei","doi":"10.22130/SCMA.2018.88329.461","DOIUrl":"https://doi.org/10.22130/SCMA.2018.88329.461","url":null,"abstract":"In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied. Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of values of basic A-factor block circulant matrices are investigated.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"55-68"},"PeriodicalIF":0.0,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49241165","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 : 2019-12-17DOI: 10.22130/SCMA.2018.92986.488
N. Taş, N. Özgür
Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems using different techniques by means of new generalized contractive conditions and the notion of the closed ball. Our results generalize and improve some known fixed point results. We provide some illustrative examples to show the validity of our definitions and fixedpoint theorems.
{"title":"Common Fixed Point Results on Complex-Valued $S$-Metric Spaces","authors":"N. Taş, N. Özgür","doi":"10.22130/SCMA.2018.92986.488","DOIUrl":"https://doi.org/10.22130/SCMA.2018.92986.488","url":null,"abstract":"Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems using different techniques by means of new generalized contractive conditions and the notion of the closed ball. Our results generalize and improve some known fixed point results. We provide some illustrative examples to show the validity of our definitions and fixedpoint theorems.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"83-105"},"PeriodicalIF":0.0,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47563894","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 : 2019-12-17DOI: 10.22130/SCMA.2018.97329.523
Chander Shekhar, Sunayana Bhati, G. S. Rathore
In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ with respect to $ mu $ is given. Also, a sufficient condition for a generalized continuous $K$-frame is given. Further, among other results, we prove that generalized continuous $K$-frames are invariant under a linear homeomorphism. Finally, keeping in mind the importance of perturbation theory in various branches of applied mathematics, we study perturbation of $K$-frames and obtain conditions for the stability of generalized continuous $K$-frames.
本文定义了Hilbert空间中广义连续K-坐标系的概念。通过实例证明了广义连续K -坐标系的存在性。得到了广义连续$K$-坐标系在其坐标系算子上存在的充分必要条件，并给出了$ mathcal{H} $关于$ mu $的广义连续$K$-坐标系的刻画。同时，给出了广义连续$K$坐标系的一个充分条件。进一步证明了广义连续$K$-帧在线性同胚下是不变的。最后，考虑到微扰理论在应用数学各个分支中的重要性，我们研究了K -框架的微扰，得到了广义连续K -框架稳定性的条件。
{"title":"Generalized Continuous Frames for Operators","authors":"Chander Shekhar, Sunayana Bhati, G. S. Rathore","doi":"10.22130/SCMA.2018.97329.523","DOIUrl":"https://doi.org/10.22130/SCMA.2018.97329.523","url":null,"abstract":"In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ with respect to $ mu $ is given. Also, a sufficient condition for a generalized continuous $K$-frame is given. Further, among other results, we prove that generalized continuous $K$-frames are invariant under a linear homeomorphism. Finally, keeping in mind the importance of perturbation theory in various branches of applied mathematics, we study perturbation of $K$-frames and obtain conditions for the stability of generalized continuous $K$-frames.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45987630","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 : 2019-12-16DOI: 10.22130/SCMA.2019.97961.527
Mensur Tugba Yalcin, H. Simsek, I. Altun
In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the quasi metric does not provide the symmetry property. Finally, we show that our main results includes many fixed point theorems presented on both complete metric and complete quasi metric spaces in the literature. We also provide an illustrative example to show importance of our results.
{"title":"Fixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions","authors":"Mensur Tugba Yalcin, H. Simsek, I. Altun","doi":"10.22130/SCMA.2019.97961.527","DOIUrl":"https://doi.org/10.22130/SCMA.2019.97961.527","url":null,"abstract":"In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the quasi metric does not provide the symmetry property. Finally, we show that our main results includes many fixed point theorems presented on both complete metric and complete quasi metric spaces in the literature. We also provide an illustrative example to show importance of our results.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"23-36"},"PeriodicalIF":0.0,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44209520","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 : 2019-12-16DOI: 10.22130/SCMA.2019.93964.499
T. Sow
In this paper, we introduce two iterative schemes by a modified Krasnoselskii-Mann algorithm for finding a common element of the set of solutions of equilibrium problems and the set of fixed points of multivalued nonexpansive mappings in Hilbert space. We prove that the sequence generated by the proposed method converges strongly to a common element of the set of solutions of equilibruim problems and the set of fixed points of multivalued nonexpansive mappings which is also the minimum-norm element of the above two sets. Finally, some applications of our results to optimization problems with constraint and the split feasibility problem are given. No compactness assumption is made. The methods in the paper are novel and different from those in early and recent literature.
{"title":"A New Iterative Algorithm for Multivalued Nonexpansive Mappping and Equlibruim Problems with Applications","authors":"T. Sow","doi":"10.22130/SCMA.2019.93964.499","DOIUrl":"https://doi.org/10.22130/SCMA.2019.93964.499","url":null,"abstract":"In this paper, we introduce two iterative schemes by a modified Krasnoselskii-Mann algorithm for finding a common element of the set of solutions of equilibrium problems and the set of fixed points of multivalued nonexpansive mappings in Hilbert space. We prove that the sequence generated by the proposed method converges strongly to a common element of the set of solutions of equilibruim problems and the set of fixed points of multivalued nonexpansive mappings which is also the minimum-norm element of the above two sets. Finally, some applications of our results to optimization problems with constraint and the split feasibility problem are given. No compactness assumption is made. The methods in the paper are novel and different from those in early and recent literature.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"1-22"},"PeriodicalIF":0.0,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45701336","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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