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Communications in Mathematical Analysis最新文献

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Fixed Points of $p$-Hybrid $L$-Fuzzy Contractions $p$-混合$L$-模糊收缩的不动点
Communications in Mathematical Analysis Pub Date : 2021-06-09 DOI: 10.22130/SCMA.2021.137899.863
S. Mohammed, I. A. Fulatan, Yahaya Sirajo
{"title":"Fixed Points of $p$-Hybrid $L$-Fuzzy Contractions","authors":"S. Mohammed, I. A. Fulatan, Yahaya Sirajo","doi":"10.22130/SCMA.2021.137899.863","DOIUrl":"https://doi.org/10.22130/SCMA.2021.137899.863","url":null,"abstract":"In this paper, the notion of $p$-hybrid $L$-fuzzy contractions in the framework of $b$-metric space is introduced. Sufficient conditions for existence of common $L$-fuzzy fixed points under such contractions are also investigated. The established ideas are generalizations of many concepts in fuzzy mathematics. In the case where our postulates are reduced to their classical variants, the concept presented herein merges and extends several significant and well-known fixed point theorems in the setting of both single-valued and multi-valued mappings in the corresponding literature of discrete and computational mathematics.  A few of these special cases are pointed out and discussed. In support of our main hypotheses, a nontrivial example is provided.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44881381","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}
引用次数: 2
Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces 大Sobolev空间中高阶椭圆型算子的内部Schauder型估计
Communications in Mathematical Analysis Pub Date : 2021-05-01 DOI: 10.22130/SCMA.2021.521544.893
B. Bilalov, S. Sadigova
{"title":"Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces","authors":"B. Bilalov, S. Sadigova","doi":"10.22130/SCMA.2021.521544.893","DOIUrl":"https://doi.org/10.22130/SCMA.2021.521544.893","url":null,"abstract":"In this paper  an elliptic operator of the $m$-th order  $L$ with continuous coefficients in the $n$-dimensional domain $Omega subset R^{n} $ in the non-standard Grand-Sobolev space $W_{q)}^{m} left(Omega right), $ generated by the norm $left| , cdot , right| _{q)} $ of the Grand-Lebesgue space $L_{q)} left(Omega right), $ is considered.  Interior  Schauder-type estimates  play a very important role in solving the Dirichlet problem for the equation $Lu=f$. The considered non-standard spaces are not separable, and therefore, to use classical methods for treating solvability problems in these spaces, one needs to modify these methods. To this aim, based on the shift operator, separable subspaces of these spaces are determined, in which finite infinitely differentiable functions are dense.  Interior  Schauder-type estimates  are established with respect to these subspaces. It should be noted that Lebesgue spaces $L_{q} left(Gright), $ are strict   parts of these subspaces. This work is a continuation of the authors  of the work cite{28}, which established the solvability in the small of higher order elliptic equations in grand-Sobolev spaces.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"129-148"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48567833","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}
引用次数: 11
Some Common Fixed Point Results for Generalized $alpha_*$-$psi$-contractive Multi-valued Mappings on Ordered Metric Spaces with Application to Initial Value Problem 有序度量空间上广义$alpha_*$-$psi$-压缩多值映射的一些公共不动点结果及其在初值问题中的应用
Communications in Mathematical Analysis Pub Date : 2021-05-01 DOI: 10.22130/SCMA.2020.121445.753
S. Pahlavany, J. H. Asl, S. Rezapour
{"title":"Some Common Fixed Point Results for Generalized $alpha_*$-$psi$-contractive Multi-valued Mappings on Ordered Metric Spaces with Application to Initial Value Problem","authors":"S. Pahlavany, J. H. Asl, S. Rezapour","doi":"10.22130/SCMA.2020.121445.753","DOIUrl":"https://doi.org/10.22130/SCMA.2020.121445.753","url":null,"abstract":"In 2012, Samet, et al. introduced the notion of $alpha$-$psi$-contractive type mappings. They have been establish some fixed point theorems for the mappings on complete metricspaces. In this paper, we introduce the notion of generalized $alpha_*$-$psi$-contractive multi-valued mappings and we give some related fixed point results on ordered metric spaces via  application to an initial value problem.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"111-128"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43502794","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}
引用次数: 0
Using Frames in Steepest Descent-Based Iteration Method for Solving Operator Equations 基于框架的最陡下降迭代法求解算子方程
Communications in Mathematical Analysis Pub Date : 2021-05-01 DOI: 10.22130/SCMA.2020.123786.771
H. Jamali, Mohsen Kolahdouz
{"title":"Using Frames in Steepest Descent-Based Iteration Method for Solving Operator Equations","authors":"H. Jamali, Mohsen Kolahdouz","doi":"10.22130/SCMA.2020.123786.771","DOIUrl":"https://doi.org/10.22130/SCMA.2020.123786.771","url":null,"abstract":"In this paper, by using the concept of frames, two iterative methods are constructed to solve the operator equation $ Lu=f $ where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint linear operator on a separable Hilbert space $ H $. These schemes are analogous with steepest descent method which is applied on a preconditioned equation obtained by frames instead. We then investigate their convergence via corresponding convergence rates, which are formed by the frame bounds. We also investigate the optimal case, which leads to the exact solution of the equation. The first scheme refers to the case where $H$ is a real separable Hilbert space, but in the second scheme, we drop this assumption.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"97-109"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48428578","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}
引用次数: 0
Coincidence Point Results for Different Types of $ H_b^{+} $-contractions on $m_b$-Metric Spaces $m_b$-度量空间上不同类型$H_b^｛+｝$-收缩的重合点结果
Communications in Mathematical Analysis Pub Date : 2021-05-01 DOI: 10.22130/SCMA.2020.131553.836
S. K. Mohanta, S. Patra
{"title":"Coincidence Point Results for Different Types of $ H_b^{+} $-contractions on $m_b$-Metric Spaces","authors":"S. K. Mohanta, S. Patra","doi":"10.22130/SCMA.2020.131553.836","DOIUrl":"https://doi.org/10.22130/SCMA.2020.131553.836","url":null,"abstract":"In this paper, we give some properties of $m_b$-metric topology and prove Cantor's intersection theorem in $m_b$-metric spaces. Moreover, we introduce some newclasses of $H_b^+ $-contractions for a pair of multi-valued and single-valued mappings and discuss their coincidence points. Some examples are provided to justify the validity of our main results.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"1-31"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41425462","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}
引用次数: 0
Two Equal Range Operators on Hilbert $C^*$-modules Hilbert $C^*$-模块上的两个等值域算子
Communications in Mathematical Analysis Pub Date : 2021-03-07 DOI: 10.22130/SCMA.2020.130093.821
A. Janfada, Javad Farokhi-ostad
{"title":"Two Equal Range Operators on Hilbert $C^*$-modules","authors":"A. Janfada, Javad Farokhi-ostad","doi":"10.22130/SCMA.2020.130093.821","DOIUrl":"https://doi.org/10.22130/SCMA.2020.130093.821","url":null,"abstract":"In this paper, number of properties, involving invertibility, existence of Moore-Penrose inverse and etc for modular operators with the same ranges on Hilbert $C^*$-modules  are presented. Natural decompositions of operators with closed range enable us to find some relations of the product of operators with  Moore-Penrose inverses under the condition that they have  the same ranges  in Hilbert $C^*$-modules. The triple reverse order law and the mixed reverse order law in the special cases are also given. Moreover, the range property and Moore-Penrose inverse are illustrated.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45597330","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}
引用次数: 0
Some Properties of Complete Boolean Algebras 完备布尔代数的一些性质
Communications in Mathematical Analysis Pub Date : 2021-02-13 DOI: 10.22130/SCMA.2020.127693.802
A. Molkhasi
{"title":"Some Properties of Complete Boolean Algebras","authors":"A. Molkhasi","doi":"10.22130/SCMA.2020.127693.802","DOIUrl":"https://doi.org/10.22130/SCMA.2020.127693.802","url":null,"abstract":"The main result of this paper is a characterization of the strongly algebraically closed algebras in the  lattice of all real-valued continuous functions and the equivalence classes of $lambda$-measurable. We shall provide conditions  which strongly algebraically closed algebras carry a strictly positive Maharam submeasure. Particularly, it is proved that if $B$ is a strongly algebraically closed lattice  and $(B,, sigma)$ is a Hausdorff space  and $B$ satisfies  the   $G_sigma$ property, then $B$ carries a strictly positive Maharam submeasure.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49292980","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}
引用次数: 0
Second Module Cohomology Group of Induced Semigroup Algebras 诱导半群代数的第二模上同调群
Communications in Mathematical Analysis Pub Date : 2021-02-13 DOI: 10.22130/SCMA.2020.130935.826
Mohammad Rrza Miri, E. Nasrabadi, Kianoush Kazemi
{"title":"Second Module Cohomology Group of Induced Semigroup Algebras","authors":"Mohammad Rrza Miri, E. Nasrabadi, Kianoush Kazemi","doi":"10.22130/SCMA.2020.130935.826","DOIUrl":"https://doi.org/10.22130/SCMA.2020.130935.826","url":null,"abstract":"For a discrete semigroup $ S $ and a left multiplier operator  $T$ on  $S$, there is a new induced semigroup $S_{T}$, related to $S$ and $T$. In this paper, we show that if $T$ is multiplier and bijective,  then the second module cohomology groups $mathcal{H}_{ell^1(E)}^{2}(ell^1(S), ell^{infty}(S))$ and $mathcal{H}_{ell^1(E_{T})}^{2}(ell^1({S_{T}}), ell^{infty}(S_{T}))$ are equal, where $E$ and  $E_{T}$ are subsemigroups of idempotent elements in $S$ and $S_{T}$,   respectively.  Finally, we show thet, for every odd $ninmathbb{N}$,  $mathcal{H}_{ell^1(E_{T})}^{2}(ell^1(S_{T}),ell^1(S_{T})^{(n)})$ is a Banach space, when $S$ is a commutative inverse semigroup.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46874723","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}
引用次数: 0
Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial $b_{v}left( sright) $-Metric Spaces 完全偏$b_{v}左(右)$-度量空间中geragty型收缩映射的不动点定理
Communications in Mathematical Analysis Pub Date : 2021-02-13 DOI: 10.22130/SCMA.2020.127414.799
Ebru Altiparmak, Ibrahim Karahan
{"title":"Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial $b_{v}left( sright) $-Metric Spaces","authors":"Ebru Altiparmak, Ibrahim Karahan","doi":"10.22130/SCMA.2020.127414.799","DOIUrl":"https://doi.org/10.22130/SCMA.2020.127414.799","url":null,"abstract":"In this paper, necessary and sufficient conditions for the existence and uniqueness of fixed points of generalized Geraghty type contraction mappings are given in complete partial $b_{v}(s) $-metric spaces. The results are more general than several results that exist in the literature because of the considered space. A numerical example is given to support the obtained results. Also, the existence and uniqueness of the solutions of an integral equation has been verified considered as an application.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44478636","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}
引用次数: 0
A Fixed Point Theorem for Weakly Contractive Mappings 弱压缩映射的一个不动点定理
Communications in Mathematical Analysis Pub Date : 2021-02-01 DOI: 10.22130/SCMA.2020.124853.778
M. Saheli, Seyed Ali Mohammad, Mohsenialhosseini
{"title":"A Fixed Point Theorem for Weakly Contractive Mappings","authors":"M. Saheli, Seyed Ali Mohammad, Mohsenialhosseini","doi":"10.22130/SCMA.2020.124853.778","DOIUrl":"https://doi.org/10.22130/SCMA.2020.124853.778","url":null,"abstract":"In this paper, we generalize the concepts of weakly Kannan, weakly Chatterjea and weakly Zamfirescu for fuzzy metric spaces. Also, we investigate Banach's fixed point theorem for the mentioned classes of functions in these spaces. Moreover, we show that the class of weakly Kannan and weakly Chatterjea maps are subclasses of the class of weakly Zamfirescu maps.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"107-122"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42388520","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}
引用次数: 0
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