Topological Algebra and its Applications

Aron, David; Kumar, Santosh

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2020-0108

AbstractIn this paper, a common fixed point theorem is demonstrated for a sequence of multivalued mappings which satisfy certain requirements in complete metric spaces. The results proved here will generalize and extend the results due to Ćirić [1]. Suitable examples are given at the end to support the results proved herein.

Öztürk, Mahpeyker; Girgin, Ekber

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2020-0109

AbstractIn this study, we demonstrate the existence and uniqueness of common fixed points of a generalized (α,β)− simulation contraction on a non-Archimedean modular metric space. We achieve some consequences in non-Archimedean modular metric spaces as an application, using the structure of a directed graph. Eventually, we contemplate the existence of solutions to a class of functional equations standing up dynamic programming with the help of our outcomes.

Averbukh, Boris G.

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2020-0110

AbstractExtensions of a given topological monoid where all its unitary Cauchy filters converge, can induce di˙erent topologies on its underlying set. We study properties of these topologies and prove a condition under which the initial topology of this monoid is one of them.

Tufa, Abebe Regassa

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0111

AbstractIn this paper, we introduce new iterative methods for approximating common fixed points of two non-self mappings in the framework of real Hilbert spaces. We establish weak and strong convergence results for approximating common fixed points of two nonexpansive non-self mappings. In addition, we establish strong convergence results for approximating common fixed points of two quasi-nonexpansive non-self mappings under appropriate conditions. Our results improve and generalize many of the results in the literature. Moreover, our findings will open the way forward for the study of iterative methods for finding common fixed points of two non-self mappings in Banach spaces more general than Hilbert spaces.

Diphofu, T.; Kaelo, P.; Tufa, A.R.

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0112

AbstractConjugate 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.

Altun, Ishak; Erduran, Ali

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0114

AbstractThis 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.

Park, Sehie

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0113

AbstractAccording 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.

Bouriah, Soufyane; Salim, Abdelkrim; Benchohra, Mouffak

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0115

AbstractIn this paper, we establish the existence of solutions for a class of nonlinear implicit neutral fractional differential equations with terminal condition and Hilfer-Katugampola fractional derivative. The Banach contraction principle and Krasnoselskii’s fixed point theorem are used to support the arguments. An illustration is provided to demonstrate the relevance of our results.

Fernandez, Jerolina; Malviya, Neeraj; Kumar, Santosh

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0116

AbstractIn this manuscript, we present a new notion which is named as extended Nb-cone metric space over Banach algebra and investigate some fixed point results in the new setting. In order to examine the validity of the underlying space we gave an application for existence and uniqueness of solution for a system of Fredholm integral equation. At last, we present some interesting examples to illustrate our work.

Patil, Jayashree; Hardan, Basel; Hamoud, Ahmed A.; Bachhav, Amol; Emadifar, Homan

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0117

AbstractIn this work, a new common fixed point result by generalized contractive functions fulfilling the type of admissibility condition in a Hausdorff Branciari metric space with the support of C-functions, was obtained.

Mewomo, Oluwatosin Temitope; Leyew, Bahru Tsegaye; Abbas, Mujahid

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0118

AbstractIn 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.

Maphane, Oteng; Gatsinzi, Jean-Baptiste

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0119

AbstractWe 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.

Wangwe, Lucas

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0120

AbstractThe aim of this paper is to prove fixed point results for Interpolativemappings in F-Mv-metric spaces with an application which cannot be obtained from the corresponding results in metric spaces. We also provide an illustrative example to support our results. Besides discussing an application to Volterra-Fredholm type integral equations.

Roy, Bishwambhar; Sen, Ritu

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0121

AbstractIn 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.

Ullah, Kifayat; Katiyar, S. K.

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0123

AbstractIn 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.

Abass, H.A.; Jolaoso, L. O.; Mewomo, O. T.

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0124

AbstractIn 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.

Massamba, Fortuné; Ssekajja, Samuel

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0126

AbstractWe introduce a geometric flow on a screen integrable null hypersurface in terms of its local second fundamental form. We use it to give an alternative proof to the vorticity free Raychaudhuri’s equation for null hypersurface, as well as establishing conditions for the existence of constant mean curvature (CMC) null hypersurfaces, and leaves of constant scalar curvatures.

Gubena, Yeshiwas Mebrat; Alemayehu, Teferi Getachew; Wondifraw, Yohannes Gedamu

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0128

AbstractIn 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.

Acar, Özlem

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0129

AbstractThe 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.

Gutik, Oleg; Khylynskyi, Pavlo

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0130

AbstractLet 𝒞ℕ be a monoid which is generated by the partial shift α : n↦n +1 of the set of positive integers ℕ and its inverse partial shift β : n + 1 ↦n. In this paper we prove that if S is a submonoid of the monoid Iℕ∞ of all partial cofinite isometries of positive integers which contains Cscr;ℕ as a submonoid then every Hausdorff locally compact shift-continuous topology on S with adjoined zero is either compact or discrete. Also we show that the similar statement holds for a locally compact semitopological semigroup S with an adjoined compact ideal.

Robdera, Mangatiana A.

2022 Topological Algebra and its Applications

doi: 10.1515/taa-2022-0131

AbstractWe show that the many of the canonical quantifications of interrelated concepts, centered around compactness in the setting of metric spaces, can be easily generalized to the setting of topological linear spaces. Among other things, we obtain a generalization of the Hausdorff Total Boundedness Principle, of the Grothendieck Compactness Principle, as well as of the Convex Compactness Principle for topological vector spaces.