Pub Date : 2021-06-09DOI: 10.22130/SCMA.2021.137899.863
S. Mohammed, I. A. Fulatan, Yahaya Sirajo
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.
{"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}
Pub Date : 2021-05-01DOI: 10.22130/SCMA.2021.521544.893
B. Bilalov, S. Sadigova
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.
{"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}
Pub Date : 2021-05-01DOI: 10.22130/SCMA.2020.121445.753
S. Pahlavany, J. H. Asl, S. Rezapour
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.
{"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}
Pub Date : 2021-05-01DOI: 10.22130/SCMA.2020.123786.771
H. Jamali, Mohsen Kolahdouz
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.
本文利用坐标系的概念，构造了求解算子方程$ Lu=f $的两种迭代方法，其中$ L:Hrightarrow H $是可分离Hilbert空间$ H $上的有界可逆自伴随线性算子。这些格式与最陡下降法类似，而最陡下降法应用于由帧得到的预条件方程。然后我们通过相应的收敛率来研究它们的收敛性，这些收敛率由框架界形成。我们还研究了最优情况，从而得到了方程的精确解。第一种方案是指$H$是实可分离希尔伯特空间的情况，但在第二种方案中，我们放弃了这个假设。
{"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}
Pub Date : 2021-05-01DOI: 10.22130/SCMA.2020.131553.836
S. K. Mohanta, S. Patra
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.
{"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}
Pub Date : 2021-03-07DOI: 10.22130/SCMA.2020.130093.821
A. Janfada, Javad Farokhi-ostad
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.
{"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}
Pub Date : 2021-02-13DOI: 10.22130/SCMA.2020.127693.802
A. Molkhasi
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.
{"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}
Pub Date : 2021-02-13DOI: 10.22130/SCMA.2020.130935.826
Mohammad Rrza Miri, E. Nasrabadi, Kianoush Kazemi
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.
{"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}
Pub Date : 2021-02-13DOI: 10.22130/SCMA.2020.127414.799
Ebru Altiparmak, Ibrahim Karahan
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.
{"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}
Pub Date : 2021-02-01DOI: 10.22130/SCMA.2020.124853.778
M. Saheli, Seyed Ali Mohammad, Mohsenialhosseini
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.
{"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}
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