{"title":"Fixed point results for generalized multivalued orthogonal α-F-contraction of integral type mappings in orthogonal metric spaces","authors":"O. Mewomo, Bahru Tsegaye Leyew, M. Abbas","doi":"10.1515/taa-2022-0118","DOIUrl":"https://doi.org/10.1515/taa-2022-0118","url":null,"abstract":"Abstract In the present article, we introduce a new type of generalized multivalued orthogonal α-Fcontraction of integral type mappings in the context of orthogonal metric spaces and establish some fixed point results. We construct an example to show the existence of the new type of mappings introduce in this work. Our results substantially unify, generalize and complement the comparable results in the existing literature. As an application of our results, we derive periodic point results for the generalized single valued orthogonal α-F-contraction of integral type mappings in orthogonal metric spaces.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"10 1","pages":"113 - 131"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45274106","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}
Y. M. Gubena, Teferi Getachew Alemayehu, Y. G. Wondifraw
{"title":"Closure Fuzzy Filters of Decomposable MS-Algebras","authors":"Y. M. Gubena, Teferi Getachew Alemayehu, Y. G. Wondifraw","doi":"10.1515/taa-2022-0128","DOIUrl":"https://doi.org/10.1515/taa-2022-0128","url":null,"abstract":"Abstract In this paper, we give some results of closure fuzzy filters of decomposable MS-algebras, characterization of closure fuzzy filters, and homomorphism of closure fuzzy filters. It is observed that the class of all closure fuzzy filters of a decomposable MS-algebra forms a bounded distributive lattice. We have also characterized the class of all closure fuzzy filters of a decopmposable MS-algebra in terms of boosters. Some properties of the homomorphic images and the inverse images of closure fuzzy filters are studied.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"10 1","pages":"216 - 226"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47643130","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":"Some fixed point results on Ultrametric Space","authors":"Ö. Acar","doi":"10.1515/taa-2022-0129","DOIUrl":"https://doi.org/10.1515/taa-2022-0129","url":null,"abstract":"Abstract The present paper deals with new fixed point theorems by means of F−contraction. The results are present in spherically complete ultrametric space for single valued rational type mappings. The special cases of the results which reduce the existing ones are presented and some examples are given to illustrating our results.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"10 1","pages":"227 - 232"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45060544","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":"Two fixed point results on F-metric spaces","authors":"I. Altun, A. Erduran","doi":"10.1515/taa-2022-0114","DOIUrl":"https://doi.org/10.1515/taa-2022-0114","url":null,"abstract":"Abstract This paper presents two fixed point results for both single valued and multivalued mappings on F-metric spaces, which is introduced by Jleli and Samet [1]. First, we consider the concept of P-contraction for single valued mappings. Then using the Feng-Liu’s technique, we present a fixed point result for F-closed set valued mappings on F-metric spaces.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"10 1","pages":"61 - 67"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45863746","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":"Equivalents of maximum principles for several spaces","authors":"Sehie Park","doi":"10.1515/taa-2022-0113","DOIUrl":"https://doi.org/10.1515/taa-2022-0113","url":null,"abstract":"Abstract According to our long-standing Metatheorem, certain maximum theorems can be equivalently reformulated to various types of fixed point theorems, and conversely. As examples of such theorems, in this paper, we list Zermelo’s fixed point theorem, Brøndsted’s principle, Fang’s F-type theorem, related theorems for locally convex spaces and quasi-uniform spaces. Further we review some few works concerned with our Metatheorem.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"10 1","pages":"68 - 76"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41943532","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":"On ω*-open sets and decomposition of continuity","authors":"B. Roy, R. Sen","doi":"10.1515/taa-2022-0121","DOIUrl":"https://doi.org/10.1515/taa-2022-0121","url":null,"abstract":"Abstract In this paper our main interest is to introduce a new topology on an ideal topological space.We have studied some properties of this newly defined topology. It is shown that X is Lindelöf with respect to this new topology if and only if it is Lindelöf with respect to the old one.We have introduced and studied ω*-continuity and some related notions. Finally we have given decomposition theorem for continuity and ω*-continuity.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"10 1","pages":"154 - 160"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43201600","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":"Convergence analysis for split hierachical monotone variational inclusion problem in Hilbert spaces","authors":"H. Abass, L. Jolaoso, O. Mewomo","doi":"10.1515/taa-2022-0124","DOIUrl":"https://doi.org/10.1515/taa-2022-0124","url":null,"abstract":"Abstract In this paper, we introduce a new iterative algorithm for approximating a common solution of Split Hierarchical Monotone Variational Inclusion Problem (SHMVIP) and Fixed Point Problem (FPP) of k-strictly pseudocontractive mappings in real Hilbert spaces. Our proposed method converges strongly, does not require the estimation of operator norm and it is without imposing the strict condition of compactness; these make our method to be potentially more applicable than most existing methods in the literature. Under standard and mild assumption of monotonicity of the SHMVIP associated mappings, we establish the strong convergence of the iterative algorithm.We present some applications of our main result to approximate the solution of Split Hierarchical Convex Minimization Problem (SHCMP) and Split Hierarchical Variational Inequality Problem (SHVIP). Some numerical experiments are presented to illustrate the performance and behavior of our method. The result presented in this paper extends and complements some related results in literature.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"10 1","pages":"167 - 184"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67317591","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":"A convergent hybrid three-term conjugate gradient method with sufficient descent property for unconstrained optimization","authors":"T. Diphofu, P. Kaelo, A. Tufa","doi":"10.1515/taa-2022-0112","DOIUrl":"https://doi.org/10.1515/taa-2022-0112","url":null,"abstract":"Abstract Conjugate gradient methods are very popular for solving large scale unconstrained optimization problems because of their simplicity to implement and low memory requirements. In this paper, we present a hybrid three-term conjugate gradient method with a direction that always satisfies the sufficient descent condition. We establish global convergence of the new method under the weak Wolfe line search conditions. We also report some numerical results of the proposed method compared to relevant methods in the literature.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"10 1","pages":"47 - 60"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43334169","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":"Cyclic weak ϕ iterated function system","authors":"K. Ullah, S. Katiyar","doi":"10.1515/taa-2022-0123","DOIUrl":"https://doi.org/10.1515/taa-2022-0123","url":null,"abstract":"Abstract In this article, we are considering the cyclic weak ϕ-contraction and prove that the result is also true in Hausdorff metric space. We are constructing a cyclic weak ϕ iterated function system (IFS), which gives the self-referential set or attractor, called the fractal.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"10 1","pages":"161 - 166"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47566021","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":"On the Hochschild cohomology of a map between commutative differential graded algebras","authors":"O. Maphane, J. Gatsinzi","doi":"10.1515/taa-2022-0119","DOIUrl":"https://doi.org/10.1515/taa-2022-0119","url":null,"abstract":"Abstract We consider a surjective morphism between commutative differential graded algebras ϕ: (∧V, d) → (B, d), where V is finite dimensional, and (B, d) is a module over ∧V via the mapping ϕ. We show that the Hochschild cohomology HH*(∧V; B) can be computed in terms of the graded vector space of positive ϕ-derivations. Moreover, if V is finite dimensional, then HH*(∧V; B) contains a polynomial algebra.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"10 1","pages":"132 - 140"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49324507","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}