Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 

Saved Queries

Sign in to use this feature.

Search Filter Reset All

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Subjects Reset
Select Subjects

Journals

remove_circle_outline
remove_circle_outline
Add Journals Reset
Select Journals

Article Types

remove_circle_outline
Add Article Types Reset
Select Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Countries / Regions Reset
Select Countries / Regions
Update Search
share announcement

Search Results (5)

Search Parameters:
Keywords = F -bipolar metric space

Order results
Result details
Results per page
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
19 pages, 325 KB  
Article
Existence and Uniqueness of Fixed-Point Results in Non-Solid C⋆-Algebra-Valued Bipolar b-Metric Spaces
by Annel Thembinkosi Bokodisa and Maggie Aphane
Mathematics 2025, 13(4), 667; https://doi.org/10.3390/math13040667 - 18 Feb 2025
Viewed by 1153
Abstract
In this monograph, motivated by the work of Aphane, Gaba, and Xu, we explore fixed-point theory within the framework of C⋆-algebra-valued bipolar b-metric spaces, characterized by a non-solid positive cone. We define and analyze [...] Read more.
In this monograph, motivated by the work of Aphane, Gaba, and Xu, we explore fixed-point theory within the framework of C⋆-algebra-valued bipolar b-metric spaces, characterized by a non-solid positive cone. We define and analyze (FH−GH)-contractions, utilizing positive monotone functions to extend classical contraction principles. Key contributions include the existence and uniqueness of fixed points for mappings satisfying generalized contraction conditions. The interplay between the non-solidness of the cone, the C⋆-algebra structure, and the completeness of the space is central to our results. We apply our results to find uniqueness of solutions to Fredholm integral equations and differential equations, and we extend the Ulam–Hyers stability problem to non-solid cones. This work advances the theory of metric spaces over Banach algebras, providing foundational insights with applications in operator theory and quantum mechanics. Full article
►▼ Show Figures

Figure 1

11 pages, 275 KB  
Article
Fixed-Point Results of F-Contractions in Bipolar p-Metric Spaces
by Nabanita Konwar and Pradip Debnath
Axioms 2024, 13(11), 773; https://doi.org/10.3390/axioms13110773 - 8 Nov 2024
Viewed by 1081
Abstract
In this paper, we present new findings on F-contraction in bipolar p-metric spaces. We establish a covariant Banach-type fixed-point theorem and a contravariant Reich-type fixed-point theorem based on F-contraction in these spaces. Additionally, we include an example that demonstrates the [...] Read more.
In this paper, we present new findings on F-contraction in bipolar p-metric spaces. We establish a covariant Banach-type fixed-point theorem and a contravariant Reich-type fixed-point theorem based on F-contraction in these spaces. Additionally, we include an example that demonstrates the applicability of our results. Our results non-trivially extend this covariant Banach-type fixed-point theorem and contravariant Reich type theorem via the concept of F-contraction. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
17 pages, 301 KB  
Article
F-Bipolar Metric Spaces: Fixed Point Results and Their Applications
by Badriah Alamri
Axioms 2024, 13(9), 609; https://doi.org/10.3390/axioms13090609 - 9 Sep 2024
Cited by 1 | Viewed by 1425
Abstract
The aim of this research article is to broaden the scope of fixed point theory in F-bipolar metric spaces by introducing the concept of rational (⋏,⋎,ψ)-contractions. These new contractions allow for the formulation of fixed point [...] Read more.
The aim of this research article is to broaden the scope of fixed point theory in F-bipolar metric spaces by introducing the concept of rational (⋏,⋎,ψ)-contractions. These new contractions allow for the formulation of fixed point theorems specifically designed for contravariant mappings. The validity of our approach is substantiated by a meticulously crafted example. Moreover, we explore the practical implications of these theorems beyond the realm of fixed point theory. Notably, we demonstrate their effectiveness in establishing the existence and uniqueness of solutions to integral equations. Additionally, we investigate homotopy problems, focusing on the conditions for the existence of a unique solution within this framework. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics IV)
19 pages, 326 KB  
Article
Solving Integral Equation and Homotopy Result via Fixed Point Method
by Badriah Alamri
Mathematics 2023, 11(21), 4408; https://doi.org/10.3390/math11214408 - 24 Oct 2023
Cited by 1 | Viewed by 1488
Abstract
The aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of (α,η,ψ)-contraction in the framework [...] Read more.
The aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of (α,η,ψ)-contraction in the framework of F-bipolar metric space and prove some fixed point results for covariant and contravariant mappings. Some coupled fixed point results in F-bipolar metric space are derived as outcomes of our principal theorems. A non-trivial example is also provided to validate the authenticity of the established results. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
14 pages, 302 KB  
Article
Fixed Point Results in F-Bipolar Metric Spaces with Applications
by Badriah Alamri
Mathematics 2023, 11(10), 2399; https://doi.org/10.3390/math11102399 - 22 May 2023
Cited by 4 | Viewed by 1953
Abstract
The aim of this research article is to obtain fixed point results in the context of F-bipolar metric spaces. The obtained results extend some fixed point theorems in the existing literature. We also provide a non-trivial example to validate our claims. The [...] Read more.
The aim of this research article is to obtain fixed point results in the context of F-bipolar metric spaces. The obtained results extend some fixed point theorems in the existing literature. We also provide a non-trivial example to validate our claims. The existence and uniqueness of the solution of the integral equation are proved as applications of our leading results. Furthermore, the existence of the unique solution in homotopy theory is also investigated. Full article
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying article 1-50 on page 1 of 1.
Back to TopTop