journal: Topological Algebra and its Applications

Open Access Published since May 6, 2013

Topological Algebra and its Applications

ISSN: 2299-3231

Editors-in-chief: Manuel Sanchis, Oscar Valero

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THE JOURNAL IS CLOSED FOR SUBMISSIONS

Topological Algebra and its Applications was a fully peer-reviewed open access electronic journal that published original research articles on topological-algebraic structures. This journal was devoted to the publication of original high quality research papers of moderate length in all fields of the subject.

The journal was published in Open Access model and is archived in Portico.

All authors retain copyright, unless – due to their local circumstances – their work is not copyrighted. The copyrights are governed by the Creative-Commons license.

The journal was edited by: Manuel Sanchis, University Jaume I of Castelló (Spain) and Oscar Valero, Illes Balears University (Spain)

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Volume 11 Issue 1

January 2023

Research Articles

Open Access February 18, 2023

Some fixed-point theorems for a pair of Reich-Suzuki-type nonexpansive mappings in hyperbolic spaces

Sreya Valiya Valappil, Shaini Pulickakunnel

Article number: 20220132

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Abstract

In this article, we prove some fixed-point results for a pair of Reich-Suzuki-type nonexpansive mappings in uniformly convex W W -hyperbolic spaces. We introduce a new iterative scheme and establish its convergence to the fixed points of a pair of Reich-Suzuki-type nonexpansive mappings. We illustrate our main result with an example, and using Matlab code, it is observed that our iteration converges faster than the iteration defined by Garodia et al. for a pair of Reich-Suzuki-type nonexpansive mappings. An application is given to substantiate our main result.

Open Access February 23, 2023

Common fixed-point theorems for non-linear non-self contractive mappings in convex metric spaces

Santosh Kumar, David Aron

Article number: 20220122

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Abstract

In this article, two pairs of non-self mappings satisfying a collection of non-linear contractive conditions in convex metric space are considered to prove a common fixed-point theorem. An appropriate example is provided to support the results proved herein. In addition, we have proved a theorem as an application of our main result. Our results generalize and extend several existing theorems in the literature.

Open Access February 24, 2023

Incomplete Fermatean fuzzy preference relations and group decision-making

Necip Şimşek, Murat Kirişci

Article number: 20220125

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Abstract

There may be cases where experts do not have in-depth knowledge of the problem to be solved in decision-making problems. In such cases, experts may fail to express their views on certain aspects of the problem, resulting in incomplete preferences, in which some preference values are not provided or are missing. In this article, we present a new model for group decision-making (GDM) methods in which experts’ preferences can be expressed as incomplete Fermatean fuzzy preference relations. This model is guided by the additive-consistency property and only uses the preference values the expert provides. An additive consistency definition characterized by a Fermatean fuzzy priority vector has been given. The additive consistency property is also used to measure the level of consistency of the information provided by the experts. The proposed additive consistency definition’s property is presented, as well as a model for obtaining missing judgments in incomplete Fermatean fuzzy preference relations. We present a method for adjusting the inconsistency for Fermatean fuzzy preference relations, a model for obtaining the priority vector, and a method for increasing the consensus degrees of Fermatean fuzzy preference relations. In addition, we present a GDM method in environments with incomplete Fermatean fuzzy preference relations. To show that our method outperforms existing GDM methods in incomplete Fermatean fuzzy preference relations environments, we have provided an example and compared it with some methods. It has been seen that our proposed GDM method is beneficial for GDM in deficient Fermatean fuzzy preference relation environments and produces meaningful results for us.

Open Access March 13, 2023

A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces

Habtu Zegeye, Oganeditse A. Boikanyo

Article number: 20220133

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Abstract

In this article, we propose a Halpern-type subgradient extragradient algorithm for solving a common element of the set of solutions of variational inequality problems for continuous monotone mappings and the set of f -fixed points of continuous f -pseudocontractive mappings in reflexive real Banach spaces. In addition, we prove a strong convergence theorem for the sequence generated by the algorithm. As a consequence, we obtain a scheme that converges strongly to a common f -fixed point of continuous f -pseudocontractive mappings and a scheme that converges strongly to a common zero of continuous monotone mappings in Banach spaces. Furthermore, we provide a numerical example to illustrate the implementability of our algorithm.

Open Access June 12, 2023

Mann-Dotson's algorithm for a countable family of non-self Lipschitz mappings in hyperbolic metric space

Prashant Patel, Rahul Shukla

Article number: 20220134

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Abstract

The aim of this article is to present some Δ \Delta -convergence and strong convergence results for a countable family of non-self mappings. More precisely, we employ Mann-Dotson’s algorithm to approximate, common fixed points of a countable family of non-self L n {L}_{n} -Lipschitz mappings in hyperbolic metric spaces.

Open Access August 21, 2023

Some common fixed point theorem of rational contractive mappings in dislocated metric spaces

Uma Maheswari Jeevanandam, Anbarasan Annadurai, Gunaseelan Mani, Santosh Kumar

Article number: 20220135

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Abstract

We improve the rational contractive condition and prove the common fixed point in the dislocated metric spaces. In addition, the new generalized rational contraction has existence of a common solution for a system of integral equations.

Open Access August 27, 2023

Fixed point theorems of enriched multivalued mappings via sequentially equivalent Hausdorff metric

Mujahid Abbas, Rizwan Anjum, Muhammad Haris Tahir

Article number: 20220136

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Abstract

Recently, Abbas et al. [ Enriched multivalued contractions with applications to differential inclusions and dynamic programming , Symmetry 13 (8) (2021), 1350] obtained an interesting generalization of the Nadler fixed point theorem by introducing the concept of enriched multivalued contraction in the framework of Banach spaces. In this article, we define a new class of metrics on the family of closed and bounded subsets of a given metric space. Furthermore, fixed point theorems were established for enriched multi-valued contractions by substituting the Hausdorff metric with metrics from a specific class that are either metrically or sequentially equivalent to the Hausdorff metric. Some examples are provided to illustrate the concepts and results presented herein. These results improve, unify, and generalize several comparable results in the literature.

Open Access August 29, 2023

A variation of the class of statistical γ covers

Prasenjit Bal, Debjani Rakshit

Article number: 20230101

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Abstract

In this article, we introduce s-s- γ \gamma cover using the notion of star operator, which is an extension of the previous results on s- γ \gamma covers. We also define s-s-dense set to address the issue that a statistical dense subset of an s-s- γ \gamma cover is not an s-s- γ \gamma cover. Furthermore, we study some results on s- γ \gamma covers in subspace topology.

Open Access October 5, 2023

Fermatean fuzzy semi-prime ideals of ordered semigroups

Amal Kumar Adak, Nilkamal, Navendu Barman

Article number: 20230102

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Abstract

Fermatean fuzzy sets (FFSs) are invented to resolve the underlying limitations of intuitionistic fuzzy sets and Pythagorean fuzzy sets. The major goal of this study is to introduce Fermatean fuzzy semi-prime ideals of ordered semigroups. Fermatean fuzzy semi-prime ideals and Fermatean fuzzy prime ideals are introduced. Also, we illustrate some novel concepts to construct Fermatean fuzzy intra-regular and regular ideals. Using the conception of function of the characteristic of ordered semigroups of FFSs, we show certain fundamental facts. Several relations are given for the family of Fermatean fuzzy regular ideals of ordered semigroups.

Open Access October 5, 2023

λ-Commuting of bounded linear operators on ultrametric Banach spaces and determinant spectrum of ultrametric matrices

Jawad Ettayb

Article number: 20230103

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Abstract

In this article, we study the λ \lambda -commuting of bounded linear operators on ultrametric Banach spaces and the determinant spectrum of ultrametric matrices. We discuss some properties of λ \lambda -commuting of bounded linear operators and the determinant spectrum of ultrametric matrices. Finally, we provide some examples to support our work.

Open Access December 1, 2023

Strong fuzzy GE-filters and fuzzy GE-ideals of bordered GE-algebras

Teferi Getachew Alemayehu, Workaferahu Solomon Eshetie, Ravikumar Bandaru, Young Bae Jun

Article number: 20230104

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Abstract

The notion of strong fuzzy generalized exchange (GE)-filters and fuzzy GE-ideals of bordered GE-algebras is studied, and their related properties are investigated. We proved that the intersection of strong fuzzy GE-filters (fuzzy GE-ideals) is a strong fuzzy GE-filter (fuzzy GE-ideal). We studied the conditions for a fuzzy subset of a bordered GE-algebra to be a strong fuzzy GE-filter and the characterization of a strong fuzzy GE-filter. We studied that under some conditions, any fuzzy subset of a bordered GE-algebra can be a fuzzy GE-ideal. A given fuzzy GE-ideal and an element in a bordered fuzzy GE-algebra is established.

Open Access December 26, 2023

Fixed point results in generalized suprametric spaces

Maher Berzig

Article number: 20230105

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Abstract

We introduce the concept of generalized suprametric spaces, which subsumes some existing abstract metric spaces. Then, we show the existence of fixed points for maps satisfying nonlinear contractions involving either extended comparison or ρ \rho -subhomogeneous functions. This study was carried out in generalized suprametric spaces as well as partially ordered generalized suprametric spaces. Some related results in JS-metric spaces and in b b -suprametric spaces are improved or extended.

Open Access December 31, 2023

On the topological covering properties by means of generalized open sets

Susmita Sarkar, Prasenjit Bal, Debjani Rakshit

Article number: 20230109

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Abstract

By utilizing g g -open sets, we developed the ideas of GO-Mengerness and GO-Lindelöfness in this article. The structure of GO-compactness is compared to these topological covering features. In addition, some novel GO-compactness characterization has been investigated using nets and filter bases.

Open Access December 31, 2023

On the operator equations ABA = A² and BAB = B² on non-Archimedean Banach spaces

Jawad Ettayb

Article number: 20230110

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Abstract

Let X X and Y Y be non-Archimedean Banach spaces over K {\mathbb{K}} , A ∈ B ( X , Y ) A\in B\left(X,Y) and B ∈ B ( Y , X ) B\in B\left(Y,X) such that A B A = A 2 ABA={A}^{2} and B A B = B 2 . BAB={B}^{2}. In this article, we investigate some properties of the operator equations A B A = A 2 ABA={A}^{2} and B A B = B 2 BAB={B}^{2} , and many common basic properties of I Y − A B {I}_{Y}-AB and I X − B A {I}_{X}-BA are given. In particular, if X X and Y Y are Banach spaces over a spherically complete field K , {\mathbb{K}}, then N ( I Y − A B ) N\left({I}_{Y}-AB) is a complemented subspace of Y Y if and only if N ( I X − B A ) N\left({I}_{X}-BA) is a complemented subspace of X . X. Finally, we give some examples to illustrate our work.

Open Access December 31, 2023

Study hoop algebras by fuzzy (n-fold) obstinate filters

Ameneh Namdar, Arsham Borumand Saeid

Article number: 20230107

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Abstract

In this article, we introduce the concept of fuzzy ( n -fold) obstinate filter on hoop algebras and study some of the properties. We define and study fuzzy prime filter and fuzzy n -fold implicative filter on hoop algebras. Also, the relationship between fuzzy obstinate filter and some other fuzzy filters likeness fuzzy prime and fuzzy positive implicative filters are investigated. Then we show that the quotient of this structure is a Boolean algebra and obtained some condition equivalent with fuzzy n -fold implicative filter. Finally we show that every fuzzy n -fold obstinate filter with some conditions is a fuzzy n -fold implicative filter.

Open Access December 31, 2023

Generalized lower characteristic involving measures of non-strict singularity

Sami Baraket, Anis Ben Ghorbal, Aref Jeribi

Article number: 20230106

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Abstract

This work establishes a connection between the class of generalized lower characteristic operators and [ ⋅ ] a {\left[\cdot ]}_{a} acting on a Banach space involving measures of non-strict singularity. This study presents findings on the Jeribi essential spectra of the sum of two bounded linear operators and the Jeribi essential spectra of each operator. The results are based on certain requirements related to the measure of non-strict singularity of Fredholm inverses on a Banach space X. A particular application is provided.

Open Access December 31, 2023

Uniqueness solution for bounded n-linear functional using generalized nonexpansive type

Basel Hardan, Ahmed A. Hamoud, Jayashree Patil, Alaa A. Abdallah, Homan Emadifar, Masoumeh Khademi, Kirtiwant P. Ghadle

Article number: 20230108

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Abstract

Using the class of ( μ , σ ) \left(\mu ,\sigma ) -nonexpansive mappings, we will effectively prove the uniqueness of the approximative fixed points set for equivalent n n -linear functional spaces F {\mathscr{F}} , where F {\mathscr{F}} is nonempty and identical in every bounded case in n n -Banach space.

CiteScore	0.7	2022, Scopus (Elsevier B.V., 2023)
SCImago Journal Rank	0.243	2022, SJR (Scimago Lab, 2023; Data Source: Scopus)
Source Normalized Impact per Paper	0.928	2022, CWTS Journal Indicators (CWTS B.V., 2023; Data Source: Scopus)
Mathematical Citation Quotient	0.18
Index Copernicus Value	97.97	2022, ICI Journals Master List (Index Copernicus, 2023)

More information about journal rankings

Editorial

Editors-in-Chief
Manuel Sanchis, University Jaume I of Castelló, Spain
Oscar Valero, Illes Balears University, Spain

Editorial Advisory Board
Mati Abel, University of Tartu, Estonia
Taras Banakh, Lviv State University, Ukraine
Ismat Beg, Lahore School of Economics, Pakistan
Bachir Bekka, Rennes University, France
Dikran Dikranjan, University of Udine, Italy
Wiesław Kubiś, Czech Academy of Sciences, Czech Republic
Andrzej Łuczak, University of Lodz, Poland
Zinaida Lykova, Newcastle University, UK
Vishnu Narayan Mishra, Indira Gandhi National Tribal University, India
Rasoul Nasr-Isfahani, Isfahan University of Technology, Iran
Matthias Neufang, Carleton University, Canada
Salvador Romaguera, Polytechnic University of Valencia, Spain
Mikhail Tkachenko, University Autonoma Metropolitana, México

Advisors Editors
Kengo Matsumoto, Joetsu University of Education, Japan
Michael Megrelishvili, Bar-Ilan University, Israel
Mohammad Sal Moslehian, Ferdowsi University of Mashhad, Iran

Assistant Editor
Pedro Tirado, Polytechnic University of Valencia, Spain

Publisher
DE GRUYTER Poland
Bogumiła Zuga 32A Str.
01-811 Warsaw, Poland
T: +48 22 701 50 15

Editorial Contact
Manuel Sanchis
taa.editorial@degruyter.com

(Deutsch)

Type: Journal
Language: English
Publisher: De Gruyter Open Access
First published: May 6, 2013
Publication Frequency: 1 Issue per Year
Audience: researchers in the field of topological-algebraic structures

Topological Algebra and its Applications

Some fixed-point theorems for a pair of Reich-Suzuki-type nonexpansive mappings in hyperbolic spaces

Abstract

Common fixed-point theorems for non-linear non-self contractive mappings in convex metric spaces

Abstract

Incomplete Fermatean fuzzy preference relations and group decision-making

Abstract

A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces

Abstract

Mann-Dotson's algorithm for a countable family of non-self Lipschitz mappings in hyperbolic metric space

Abstract

Some common fixed point theorem of rational contractive mappings in dislocated metric spaces

Abstract

Fixed point theorems of enriched multivalued mappings via sequentially equivalent Hausdorff metric

Abstract

A variation of the class of statistical γ covers

Abstract

Fermatean fuzzy semi-prime ideals of ordered semigroups

Abstract

λ-Commuting of bounded linear operators on ultrametric Banach spaces and determinant spectrum of ultrametric matrices

Abstract

Strong fuzzy GE-filters and fuzzy GE-ideals of bordered GE-algebras

Abstract

Fixed point results in generalized suprametric spaces

Abstract

On the topological covering properties by means of generalized open sets

Abstract

On the operator equations ABA = A2 and BAB = B2 on non-Archimedean Banach spaces

Abstract

Study hoop algebras by fuzzy (n-fold) obstinate filters

Abstract

Generalized lower characteristic involving measures of non-strict singularity

Abstract

Uniqueness solution for bounded n-linear functional using generalized nonexpansive type

Abstract

On the operator equations ABA = A² and BAB = B² on non-Archimedean Banach spaces