Fixed Point Results Research Articles

A Symmetric View of Fixed-Point Results in Non-Archimedean Generalized Neutrosophic Metric Spaces

In this paper, we extend prominent fixed-point theorems within the framework of symmetry, a structure increasingly relevant in decision-making, optimization, and uncertainty modeling. While previous studies have explored fixed-point theorems in non-Archimedean spaces, the influence of symmetry on the properties of mappings remains underexamined. To address this gap, we introduce and analyze the concepts of χ-contractions and χ-weak contractions, demonstrating how symmetry impacts the conditions for the existence of fixed points. Our methodology integrates these concepts in generalized neutrosophic metric spaces, providing a novel perspective on fixed-point theory. We perform a rigorous analysis, revealing new insights into their practical applications. However, our proposed system may face limitations in complex or dynamic environments, where additional conditions may be necessary to ensure the existence or uniqueness of fixed points.

Fixed Point Results in Modular b-Metric-like Spaces with an Application

In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of ξ-convergence, ξ-Cauchy sequence, ξ-completeness and ξ-contraction. The existence and uniqueness of fixed points in the modular b-metric-like space are handled. Moreover, we give some examples and an application to an integral equation to illustrate the usability of the obtained results.

Fixed Point Results for Fuzzy Enriched Contraction in Fuzzy Banach Spaces with Applications to Fractals and Dynamic Market Equillibrium

We introduce fuzzy enriched contraction, which extends the classical notion of fuzzy Banach contraction and encompasses specific fuzzy non-expansive mappings. Our investigation establishes both the presence and uniqueness of fixed points considering this broad category of operators using a Krasnoselskij iterative scheme for their approximation. We also show the graphical representation of fuzzy enriched contraction and analyze its graph for different values of beta. The implications of these findings extend to significant results within fuzzy fixed-point theory, enriching the understanding of iterative processes in fuzzy metric spaces. To demonstrate the versatility of our innovative concepts and the associated fixed-point theorems, we provide illustrative examples that showcase their applicability across diverse domains, including the generation of fractals. This demonstrates the relevance of fuzzy enriched contraction to iterated function systems, enabling the study of fractal structures under various contractive conditions. Additionally, we explore practical applications of fuzzy enriched contraction in dynamic market equilibrium, offering new insights into stability and convergence in economic models. Through this unified framework, we open new avenues for both theoretical advancements and real world applications in fuzzy systems.

Convergence of Graph-Based Fixed Point Results with Application to Fredholm Integral Equation

In this manuscript, we present a novel concept termed graphical Θc-Kannan contraction within the context of graphically controlled metric-type spaces. Unlike traditional Kannan contraction, this novel concept presents a modified method of contraction mapping. We discuss the significance and the existence of fixed point results within the framework of this novel contraction. To strengthen the credibility of our theoretical remarks, we provide a comparison example demonstrating the efficiency of our suggested framework. Our study not only broadens the theoretical foundations inside graphically controlled metric-type spaces by introducing and examining visual Θc-Kannan contraction, but it also demonstrates the practical significance of our innovations through significant examples. Furthermore, applying our findings to second-order differential equations by constructing integral equations into the domain of Fredholm sheds light on the broader implications of our research in the field of mathematical analysis and contributes to the advancement of this field.

Investigating fractal fractional PDEs, electric circuits, and integral inclusions via (ψ,ϕ)-rational type contractions

The fixed point theory has been generalized mainly in two directions. One is the extension of the spaces, and the other is relaxing and generalizing the contractions. This paper aims to establish novel fixed point results of rational type generalized (ψ,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\psi ,\\phi )$$\\end{document}-contractions in the context of extended b-metric spaces. This will allow us to analyze generalized rational type contraction in a more relaxed and diversified framework in the light of the characteristics of (ψ,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\psi ,\\phi )$$\\end{document}. Some existing rational-type contractions have been recalled in this direction, and others are defined. New fixed point results have been established by utilizing the properties of ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi$$\\end{document} and ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi$$\\end{document} and applying the iteration technique. Moreover, the established results are employed to investigate the stability of fractal and fractional differential equations and electric circuits. For the reliability of the established results, examples and applications to the system of integral inclusions and system of integral equations are presented.

Fixed Point Results of Fuzzy Multivalued Graphic Contractive Mappings in Generalized Parametric Metric Spaces

Fixed Point Results of Fuzzy Multivalued Graphic Contractive Mappings in Generalized Parametric Metric Spaces

Fixed Point Results for Almost Contraction Mappings in Fuzzy Metric Space

في بعض المسائل الرياضية والحاسوبية والاقتصادية والنمذجة، يكون وجود حل لمشكلة نظرية أو مشكلة في العالم الحقيقي مرادفًا لوجود نقطة صامدة (Fp) لدالة مناسبة. وبالتالي، فأن نظرية النقطة الصامدة Fp تلعب دورًا أساسيًا في مجموعة واسعة من السياقات الرياضية والعلمية. تعتبر نظرية النقطة الصامدة Fp في حد ذاتها مزيجًا مذهلاً مكون من التحليل (التحليل الصرف والتحليل التطبيقي)، والهندسة، والطوبولوجيا. لقد أظهرت السنوات الأخيرة أن نظرية النقطة الصامدة Fp هي أداة قوية ومفيدة للغاية في دراسة الحالات غير الخطية. تهتم نظريات النقطة الصامدة Fp بدالة f من المجموعة X الى المجموعة X نفسها والتي في ظل ظروف معينة، فأنها تسمح بوجود نقطة صامدة Fp ، بعبارة اخرى انه بمعنى لكل نقطة x موجودة في المجموعة X (x∈X) بحيث أن f(x)=x . يقدم هذا العمل ويثبت نظرية النقطة الصامدة Fp لأنواع مختلفة من دوال الانكماش في الفضاء المتري الضبابي (FM-space) والتي تسمى بدالة الانكماش القريبة ودالة الانكماش الضعيفة القريبة ( Ψ̃ ,Φ̃). في البداية، تم التذكير بمفهوم الفضاء المتري الضبابي(FM-space) وبعض المصطلحات المستخدمة في الإطار الضبابي. ثم بعد ذلك تم اعطاء مفهوم دالة المحاكاة. يتم استخدام مفهوم دالة المحاكاة هذا لتقديم تعريف دالة الانكماش Z̃ القريبة في إطار الفضاء المتري الضبابي. بالإضافة إلى ذلك، لقد تم استخدام هذا المفهوم(دالة الانكماش Z̃ القريبة) لبرهان وجود النقطة الصامدة ووحدانية النقطة الصامدة لهذا النوع من الدوال.ثم بعد ذلك تم تقديم فكرة دالة الانكماش الضعيفة القريبة ( Ψ̃ ,Φ̃) في إطار الفضاء المتري الضبابي(FM-space) ، بالإضافة إلى تقديم نظرية النقطة الصامدة Fp لهذا النوع من من الدوال. وفي نهاية البحث تم تقديم بعض الأمثلة لدعم النتائج.

On new extended cone b-metric-like spaces over a real Banach algebra

In this article, we introduce the structure of a new extended cone b-metric-like space over a Banach algebra. In this generalized space, we define the notion of generalized Reich-type mappings and prove a fixed point result. We also prove a fixed point result using α∗−ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha^{\\ast}-\\psi$\\end{document} multivalued contraction and provide some of its consequences. Finally, we furnish with applications to establish the validity of our results.

Super Metric Space and Fixed Point Results

Banach contraction principle is the beginning of the Metric fixed point theory. This principle gives existence and uniqueness of fixed points and methods for obtaining approximate fixed points. It is the basic tool of finding fixed points of all contraction type maps. It has a constructive proof which makes the theorem worthy because it yields an algorithm for computing a fixed point. Banach fixed point result has been extended by various authors in many directions either by weakening the conditions of contraction mapping or by changing the abstract structure. Several generalizations and extensions of metric spaces have been introduced. Among these, the prominent extensions are b-metric space, fuzzy metric space, partial metric space and a lot more of their combinations. In particular, a new structure namely Super metric space is introduced. In the present paper, we generalize and extend the fixed point results of fixed point theory in literature in the framework of super metric space.

Wardowski Contraction on Controlled S-Metric Type Spaces with Fixed Point Results

This article presents the concept of a triple controlled S-metric type space, characterized by three control functions: β, µ, and γ. This extends the idea of controlled S-metric type spaces. We explore several properties and provide illustrative examples. Furthermore, we introduce αs-admissible mappings and enhance Wardowski’s contraction principle by introducing (αs-F)-contractive mappings specifically designed for triple controlled S-metric type spaces. The article establishes the existence and uniqueness of fixed points within a complete triple controlled S-metric type space. Finally, we apply our main theorem to demonstrate the determination of a unique solution for an mth degree polynomial.

F-Bipolar Metric Spaces: Fixed Point Results and Their Applications

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.

Pompeiu-Hausdorff Fuzzy <i>b</i>-metric Spaces Are Associated with a Common Fixed Point and Multivalued Mappings

The notion of fuzzy logic was introduced by Zadeh. Unlike traditional logic theory, where an element either belongs to the set or does not, in fuzzy logic, the affiliation of the element to the set is expressed as a number from the interval [0, 1]. The study of the theory of fuzzy sets was prompted by the presence of uncertainty as an essential part of real-world problems, leading Zadeh to address the problem of indeterminacy. The theory of a fixed point in fuzzy metric spaces can be viewed in different ways, one of which involves the use of fuzzy logic. Fuzzy metric spaces, which are specific types of topological spaces with pleasing ”geometric” characteristics, possess a number of appealing properties and are commonly used in both pure and applied sciences. Metric spaces and their various generalizations frequently occur in computer science applications. For this reason, a new space called a Pompeiu-Hausdorff fuzzy <i>b</i>-metric space is constructed in this paper. In this space, some new fixed point results are also formulated and proven. Additionally, a general common fixed point theorem for a pair of multi-valued mappings in Pompeiu-Hausdorff fuzzy <i>b</i>-metric spaces is investigated. The findings obtained in fuzzy metric spaces, such as those discussed in Remark 3.1, are generalized by the results in this paper, and additional specific findings are produced and supported by examples. The study of denotational semantics and their applications in control theory using fuzzy <i>b</i>-metric spaces and Pompeiu-Hausdorff fuzzy <i>b</i>-metric spaces will be an important next step.

Common Fixed Point Theorems in multiplicative $\mathfrak{m}$-metric space with Applications to the System of Multiplicative Integral Equations and Numerical Results

This paper presents common fixed point results for a pair of self-mappings in multiplicative $\mathfrak{m}$-metric space. Also, we present the multiplicative partial metric structure as a specific case of a multiplicative m-metric space and demonstrate some common fixed point results. To support our conclusions, we present an illustrative example with discontinuous self-mappings. We also provide numerical iterations to approximate the common fixed point and graphs to visually substantiate our findings. As the consequences of our results, we demonstrate several common fixed point results in $m$-metric space and partial metric space. Our findings generalize various fixed point results from the literature. Furthermore, we employ the results to demonstrate the existence and uniqueness of solutions to a system of multiplicative Fredholm integral equations.

Fixed Point Results for New Classes of k-Strictly Asymptotically Demicontractive and Hemicontractive Type Multivalued Mappings in Symmetric Spaces

Fixed point theory is a significant area of mathematical analysis with applications across various fields such as differential equations, optimization, and dynamical systems. Recently, multivalued mappings have gained attention due to their ability to model more complex and realistic problems. ln this work, novel classes of nonlinear mappings called k-strictly asymptotically demicontractive-type and asymptotically hemicontractive-type multivalued mappings are introduced in real Hilbert spaces that are symmetric spaces. In addition, we discuss the weak and strong convergence results by considered modified algorithms, and a demiclosedness property, for these classes of mappings are proved. Several non-trivial examples are demonstrated to validate the newly defined mappings. Consequently, the results and iterative methods obtained in this study improve and extend several known outcomes in the literature.

Common Fixed Point Results for Contractive Mappings in Bicomplex Valued B-Metric Spaces

Common Fixed Point Results for Contractive Mappings in Bicomplex Valued B-Metric Spaces

Enriched Z-Contractions and Fixed-Point Results with Applications to IFS

In this manuscript, we initiate a large class of enriched (d,Z)-Z-contractions defined on Banach spaces and prove the existence and uniqueness of the fixed point of these contractions. We also provide an example to support our results and give an existence condition for the uniqueness of the solution to the integral equation. The results provided in the manuscript extend, generalize, and modify the existence results. Our research introduces novel fixed-point results under various contractive conditions. Furthermore, we discuss the iterated function system associated with enriched (d,Z)-Z-contractions in Banach spaces and define the enriched Z-Hutchinson operator. A result regarding the convergence of Krasnoselskii’s iteration method and the uniqueness of the attractor via enriched (d,Z)-Z-contractions is also established. Our discoveries not only confirm but also significantly build upon and broaden several established findings in the current body of literature.

Solution of an Algebraic Linear System of Equations Using Fixed Point Results in C∗-Algebra Valued Extended Branciari Sb-Metric Spaces

Solution of an Algebraic Linear System of Equations Using Fixed Point Results in C∗-Algebra Valued Extended Branciari Sb-Metric Spaces

Certain Fixed Point Results via Contraction Mappings in Neutrosophic Semi-Metric Spaces

In this work, the authors introduce the concept of neutrosophic semi-metric spaces and prove several common fixed-point theorems for countable and uncountable family of mappings via an implicit relation of contractive and integral type by utilizing locally integrable functions. These results improve and generalize the several results in the existing literature. Further, the authors present some non-trivial examples to support our main results. Mathematics Subject Classification: 46S40, 47H10, 54H25.

Generalization of Fixed-Point Results in Complex-Valued Bipolar Metric Space with Applications

Generalization of Fixed-Point Results in Complex-Valued Bipolar Metric Space with Applications

Fixed Point Results for Geraghty Type Contractions in Extended Rec-tangular Fuzzy <i>b</i>-metric Space with an Application

The aim of this paper is to define the notions of extended fuzzy b-metric spaces, fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces and to establish certain fixed point results in these settings utilizing Geraghty type contractions. We also furnished an example which illustrates our main result. To show the authenticity of our results we provide an application involving fuzzy integral equation. The obtained results generalize many existing results in the literature.