In this paper we study the existence of the fixed points for Hardy-Rogers type mappings with respect to a wt-distance in partially ordered metric spaces. Our results provide a more general statement, since we replace a w-distance with a wt-distance and ordered metric spaces with ordered b-metric spaces. Some examples are presented to validate our obtained results and an application to nonlinear fourth-order differential equation are given to support the main results.
{"title":"Fixed point results with respect to a wt-distance in partially ordered b-metric spaces and its application to nonlinear fourth-order differential equation","authors":"Reza Babaei, H. Rahimi, G. Soleimani Rad","doi":"10.4995/agt.2022.11368","DOIUrl":"https://doi.org/10.4995/agt.2022.11368","url":null,"abstract":"In this paper we study the existence of the fixed points for Hardy-Rogers type mappings with respect to a wt-distance in partially ordered metric spaces. Our results provide a more general statement, since we replace a w-distance with a wt-distance and ordered metric spaces with ordered b-metric spaces. Some examples are presented to validate our obtained results and an application to nonlinear fourth-order differential equation are given to support the main results.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"64 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77776971","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}
Chistyakov introduced and developed a concept of modular metric for an arbitrary set in order to generalise the classical notion of modular on a linear space. In this article, we introduce the theory of hyperconvexity in the setting of modular pseudometric that is herein called w-Isbell-convexity. We show that on a modular set, w-Isbell-convexity is equivalent to hyperconvexity whenever the modular pseudometric is continuous from the right on the set of positive numbers.
{"title":"On w-Isbell-convexity","authors":"O. Olela Otafudu, Katlego Sebogodi","doi":"10.4995/agt.2022.15739","DOIUrl":"https://doi.org/10.4995/agt.2022.15739","url":null,"abstract":"Chistyakov introduced and developed a concept of modular metric for an arbitrary set in order to generalise the classical notion of modular on a linear space. In this article, we introduce the theory of hyperconvexity in the setting of modular pseudometric that is herein called w-Isbell-convexity. We show that on a modular set, w-Isbell-convexity is equivalent to hyperconvexity whenever the modular pseudometric is continuous from the right on the set of positive numbers.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"30 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75342348","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}
In this paper, closed ideals in Cc(X), the functionally countable subalgebra of C(X), with the mc-topology, is studied. We show that ifX is CUC-space, then C*c(X) with the uniform norm-topology is a Banach algebra. Closed ideals in Cc(X) as a modified countable analogue of closed ideals in C(X) with the m-topology are characterized. For a zero-dimensional space X, we show that a proper ideal in Cc(X) is closed if and only if it is an intersection of maximal ideals of Cc(X). It is also shown that every ideal in Cc(X) with the mc-topology is closed if and only if X is a P-space if and only if every ideal in C(X) with the m-topology is closed. Moreover, for a strongly zero-dimensional space X, it is proved that a properly closed ideal in C*c(X) is an intersection of maximal ideals of C*c(X) if and only if X is pseudo compact. Finally, we show that if X is a P-space and F is an ec-filter on X, then F is an ec-ultrafilter if and only if it is a zc-ultrafilter.
本文研究了C(X)的函数可数子代数Cc(X)在mc-拓扑下的闭理想。证明了如果X是cc -空间，则具有一致范数拓扑的C* C (X)是Banach代数。将Cc(X)中的闭理想作为m拓扑下C(X)中的闭理想的修正可数类似物进行了表征。对于零维空间X，我们证明了Cc(X)中的固有理想当且仅当它是Cc(X)的极大理想的交集时是闭合的。还证明了C(X)中具有mc-拓扑的每个理想当且仅当X是p空间时是封闭的，当且仅当C(X)中具有m-拓扑的每个理想是封闭的。此外，对于强零维空间X，证明了C* C (X)中的适当闭理想是C* C (X)的极大理想的交，当且仅当X是伪紧的。最后，我们证明了如果X是p空间，F是X上的ec-滤波器，那么当且仅当F是zc-超滤波器时，F是ec-超滤波器。
{"title":"Closed ideals in the functionally countable subalgebra of C(X)","authors":"A. Veisi","doi":"10.4995/agt.2022.15844","DOIUrl":"https://doi.org/10.4995/agt.2022.15844","url":null,"abstract":"In this paper, closed ideals in Cc(X), the functionally countable subalgebra of C(X), with the mc-topology, is studied. We show that ifX is CUC-space, then C*c(X) with the uniform norm-topology is a Banach algebra. Closed ideals in Cc(X) as a modified countable analogue of closed ideals in C(X) with the m-topology are characterized. For a zero-dimensional space X, we show that a proper ideal in Cc(X) is closed if and only if it is an intersection of maximal ideals of Cc(X). It is also shown that every ideal in Cc(X) with the mc-topology is closed if and only if X is a P-space if and only if every ideal in C(X) with the m-topology is closed. Moreover, for a strongly zero-dimensional space X, it is proved that a properly closed ideal in C*c(X) is an intersection of maximal ideals of C*c(X) if and only if X is pseudo compact. Finally, we show that if X is a P-space and F is an ec-filter on X, then F is an ec-ultrafilter if and only if it is a zc-ultrafilter.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"39 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74049263","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}
In this paper, we propose a new iteration process which is faster than the leading S [J. Nonlinear Convex Anal. 8, no. 1 (2007), 61-79], Thakur et al. [App. Math. Comp. 275 (2016), 147-155] and M [Filomat 32, no. 1 (2018), 187-196] iterations for numerical reckoning fixed points. Using new iteration process, some fixed point convergence results for generalized α-nonexpansive mappings in the setting of uniformly convex Banach spaces are proved. At the end of paper, we offer a numerical example to compare the rate of convergence of the proposed iteration process with the leading iteration processes.
{"title":"Numerical reckoning fixed points via new faster iteration process","authors":"K. Ullah, Junaid Ahmad, F. M. Khan","doi":"10.4995/agt.2022.11902","DOIUrl":"https://doi.org/10.4995/agt.2022.11902","url":null,"abstract":"In this paper, we propose a new iteration process which is faster than the leading S [J. Nonlinear Convex Anal. 8, no. 1 (2007), 61-79], Thakur et al. [App. Math. Comp. 275 (2016), 147-155] and M [Filomat 32, no. 1 (2018), 187-196] iterations for numerical reckoning fixed points. Using new iteration process, some fixed point convergence results for generalized α-nonexpansive mappings in the setting of uniformly convex Banach spaces are proved. At the end of paper, we offer a numerical example to compare the rate of convergence of the proposed iteration process with the leading iteration processes.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82617955","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}
An almost P-space is a topological space in which every zero-set is regular-closed. We introduce a large class of spaces, C-almost P-space (briefly CAP-space), consisting of those spaces in which the closure of the interior of every zero-set is a zero-set. In this paper we study CAP-spaces. It is proved that if X is a dense and Z#-embedded subspace of a space T, then T is CAP if and only if X is a CAP and CRZ-extended in T (i.e, for each regular-closed zero-set Z in X, clTZ is a zero-set in T). In 6P.5 of [8] it was shown that a closed countable union of zero-sets need not be a zero-set. We call X a CZ-space whenever the closure of any countable union of zero-sets is a zero-set. This class of spaces contains the class of P-spaces, perfectly normal spaces, and is contained in the cozero complemented spaces and CAP-spaces. In this paper we study topological properties of CZ (resp. cozero complemented)-space and other classes of topological spaces near to them. Some algebraic and topological equivalent conditions of CZ (resp. cozero complemented)-space are characterized. Examples are provided to illustrate and delimit our results.
{"title":"Some classes of topological spaces related to zero-sets","authors":"F. Golrizkhatami, Asghar Taherifar","doi":"10.4995/agt.2022.15668","DOIUrl":"https://doi.org/10.4995/agt.2022.15668","url":null,"abstract":"An almost P-space is a topological space in which every zero-set is regular-closed. We introduce a large class of spaces, C-almost P-space (briefly CAP-space), consisting of those spaces in which the closure of the interior of every zero-set is a zero-set. In this paper we study CAP-spaces. It is proved that if X is a dense and Z#-embedded subspace of a space T, then T is CAP if and only if X is a CAP and CRZ-extended in T (i.e, for each regular-closed zero-set Z in X, clTZ is a zero-set in T). In 6P.5 of [8] it was shown that a closed countable union of zero-sets need not be a zero-set. We call X a CZ-space whenever the closure of any countable union of zero-sets is a zero-set. This class of spaces contains the class of P-spaces, perfectly normal spaces, and is contained in the cozero complemented spaces and CAP-spaces. In this paper we study topological properties of CZ (resp. cozero complemented)-space and other classes of topological spaces near to them. Some algebraic and topological equivalent conditions of CZ (resp. cozero complemented)-space are characterized. Examples are provided to illustrate and delimit our results.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"4 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78282316","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}
In this article, we provide a simple geometric proof of the following fact: The existence of transitive normalized maps induced by linear operators is possible only when the underlying space's real dimension is either 1 or 2 or infinity. A similar result holds for projective transformation as well.
{"title":"Topological transitivity of the normalized maps induced by linear operators","authors":"P. Mandal","doi":"10.4995/agt.2022.15613","DOIUrl":"https://doi.org/10.4995/agt.2022.15613","url":null,"abstract":"In this article, we provide a simple geometric proof of the following fact: The existence of transitive normalized maps induced by linear operators is possible only when the underlying space's real dimension is either 1 or 2 or infinity. A similar result holds for projective transformation as well.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78838565","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}
Recently Zhu and Zhai studied the concepts of cone b-norm and cone b-Banach space as generalizations of cone b-metric spaces and theygave a definition of ϕ-operator and obtained some new fixed point theorems in cone b-Banach spaces over Banach algebras by usingϕ-operator. In this paper we propose a notion of quasi-cone over Banach algebras, then by utilizing some new conditions andfollowing their work with introducing two mappings $mathcal{T}$ and $mathcal{S}$ we improve the fixed point theorems to the commonfixed point theorems. An example is given to illustrate the usability of the obtained results.
{"title":"Common new fixed point results on b-cone Banach spaces over Banach algebras","authors":"H. Afshari, Hadi Shojaat, A. Fulga","doi":"10.4995/agt.2022.15571","DOIUrl":"https://doi.org/10.4995/agt.2022.15571","url":null,"abstract":"Recently Zhu and Zhai studied the concepts of cone b-norm and cone b-Banach space as generalizations of cone b-metric spaces and theygave a definition of ϕ-operator and obtained some new fixed point theorems in cone b-Banach spaces over Banach algebras by usingϕ-operator. In this paper we propose a notion of quasi-cone over Banach algebras, then by utilizing some new conditions andfollowing their work with introducing two mappings $mathcal{T}$ and $mathcal{S}$ we improve the fixed point theorems to the commonfixed point theorems. An example is given to illustrate the usability of the obtained results.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"56 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72672701","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}
{"title":"Alexandroff duplicate and βκ","authors":"A. Szymanski","doi":"10.4995/agt.2022.15586","DOIUrl":"https://doi.org/10.4995/agt.2022.15586","url":null,"abstract":"We discuss spaces and the Alexandroff duplicates of those spaces that admit a Č-S embedding into the Čech-Stone compactification of a discrete space.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"83 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81710800","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}
In this paper we study the dynamics of continuous endomorphisms on Polish groups. We offer necessary and sufficient conditions for a continuous endomorphism on a Polish group to be weakly mixing. We prove that any continuous endomorphism of an abelian Polish group can be extended in a natural way to a topologically mixing endomorphism on the countable infinite product of said group.
{"title":"Topologically mixing extensions of endomorphisms on Polish groups","authors":"John Burke, Leonardo Pinheiro","doi":"10.4995/agt.2022.15187","DOIUrl":"https://doi.org/10.4995/agt.2022.15187","url":null,"abstract":"In this paper we study the dynamics of continuous endomorphisms on Polish groups. We offer necessary and sufficient conditions for a continuous endomorphism on a Polish group to be weakly mixing. We prove that any continuous endomorphism of an abelian Polish group can be extended in a natural way to a topologically mixing endomorphism on the countable infinite product of said group.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"40 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84113016","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}
A. Bera, L. Dey, S. Som, Hiranmoy Garai, W. Sintunavarat
The main aim of this paper is to study the Boyd-Wong type fixed point result in the F-metric context and apply it to obtain some existence and uniqueness criteria of solution(s) to a second order initial value problem and a Caputo fractional differential equation. We substantiate our obtained result by finding a suitable non-trivial example.
{"title":"Boyd-Wong contractions in F-metric spaces and applications","authors":"A. Bera, L. Dey, S. Som, Hiranmoy Garai, W. Sintunavarat","doi":"10.4995/agt.2022.15356","DOIUrl":"https://doi.org/10.4995/agt.2022.15356","url":null,"abstract":"The main aim of this paper is to study the Boyd-Wong type fixed point result in the F-metric context and apply it to obtain some existence and uniqueness criteria of solution(s) to a second order initial value problem and a Caputo fractional differential equation. We substantiate our obtained result by finding a suitable non-trivial example.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"390 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77121323","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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