Points For Such Mappings Research Articles

Integral Equations: New Solutions via Generalized Best Proximity Methods

This paper introduces the concept of proximal (α,F)-contractions in F-metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial example. Furthermore, we demonstrate the applicability of these results by proving the existence of solutions for Volterra integral equations related to population growth models. This approach not only extends best proximity theory, but also paves the way for further research in applied mathematics and beyond.

New L-fuzzy fixed point techniques for studying integral inclusions

The survey of the available literature shows that a lot of important invariant point problems of Banach and Heilpern types have been examined in both metric and quasimetric spaces. However, a handful of the existing results employed the recent approaches of interpolative contractions. Therefore, based on the new idea of interpolation techniques in fixed point theory, this article studies new notions of L-fuzzy contractions and investigates conditions for the existence of L-fuzzy fixed points for such mappings. On the fact that fixed points of point-to-point mappings satisfying interpolative-type contraction are not always unique, whence making the concepts more fitted for invariant point results of crisp set-valued maps, new multi-valued analogues of the key findings put forward in this work are derived. Comparative illustrations, which indicate the preeminence of the results presented herein, are constructed. From application viewpoint, one of the theorems so obtained is employed to introduce new solvability conditions of Fredholm-type integral inclusions.

ON FIXED POINTS OF INTERPOLATIVE CONVEX AND ALMOST CONVEX-TYPE CONTRACTIVE MAPPINGS

In this work, we introduce interpolative (α,q)-convex contractions and almost (α,q)-convex contractive mappings via simulation function in metric spaces and prove some existence results for fixed point of such mappings. Consequently, our results generalize numerous results in the literature.

ON L-FUZZY FIXED POINT RESULTS IN G-METRIC SPACE

Among numerous efforts in progressing fuzzy mathematics, a lot of attention has been paid to studying new L-fuzzy analogues of the conventional fixed point results and their various applications. In this note, novel concepts of L-fuzzy contractions in G-metric space is examined, and sufficient conditions for the existence of L-fuzzy fixed points for such mappings are investigated. Nontrivial examples are provided to support the assumptions of our obtained theorems. It is highlighted that the main ideas studied herein refine and include some known results in the corresponding literature. Some of these special cases of our results are pointed out and analyzed.

Some Fixed Point Theorems in S-metric Spaces via Simulation Function

We introduce the concept of generalized \(\beta\) - \(\gamma\) - Z contraction mapping with respect to a simulation function ξ and study the existence of fixed points for such mappings in complete -metric spaces. Further, we extend it to partially ordered complete -metric spaces.

Banach Contraction Principle-Type Results for Some Enriched Mappings in Modular Function Spaces

The idea of enriched mappings in normed spaces is relatively a newer idea. In this paper, we initiate the study of enriched mappings in modular function spaces. We first introduce the concepts of enriched ρ-contractions and enriched ρ-Kannan mappings in modular function spaces. We then establish some Banach Contraction Principle type theorems for the existence of fixed points of such mappings in this setting. Our results for enriched ρ-contractions are generalizations of the corresponding results from Banach spaces to modular function spaces and those from contractions to enriched ρ-contractions. We make a first ever attempt to prove existence results for enriched ρ-Kannan mappings and deduce the result for ρ-Kannan mappings. Note that even ρ-Kannan mappings in modular function spaces have not been considered yet. We validate our main results by examples.

Discussions on Proinov- C b -Contraction Mapping on b -Metric Space

In the present paper, we introduce the notion of Proinov- C b -contraction mapping and we discuss it within the most interesting abstract structure, namely, b -metric spaces. We further take into consideration the necessary conditions to guarantee the existence and uniqueness of fixed points for such mappings, as well as indicate the validity of the main results by providing illustrative examples.

On the Existence of Solutions to a Boundary Value Problem via New Weakly Contractive Operator

In this paper, the notion of generalized quasi-weakly contractive operators in metric-like spaces is introduced, and new conditions for the existence of fixed points for such mappings are investigated. A non-trivial example which highlights the novelty of our principal idea is constructed. It is observed comparatively that the proposed concepts herein subsume some important results in the corresponding literature. As an application, one of our obtained findings is utilized to setup novel criteria for the existence of solutions to two-point boundary value problems of a second order differential equation. To attract new researchers in the directions examined in this article, a significant number of corollaries are pointed out and discussed.

Hybrid Fixed Point Theorems of Fuzzy Soft Set-Valued Maps with Applications in Integral Inclusions and Decision Making

A lot of work has been completed in efforts to extend the notions of soft set and fuzzy soft set and their applications to other domains. However, neither of the two concepts has been examined in the study of functional equations in b-metric spaces. Given this background information, this paper proposes the idea of b-hybrid fuzzy soft contraction in b-metric space and investigates new criteria for the existence of fixed points for such mappings. The significance of the obtained principal result lies in the fact that the contractive inequalities can be specialized in various ways, depending on the choice of the parameters, thereby making it possible to unify, deduce, and refine several corresponding results. To motivate further studies in the directions studied herein, two applications regarding decision-making problems and an existence theorem of integral inclusion are considered, using fuzzy soft set-valued maps.

Some Extended Results for Multivalued F-Contraction Mappings

In this study, we introduce a new notion, so-called KW-type F-contraction mapping, inspired by the ideas of Wardowski and Klim–Wardowski. Then, we investigate the existence of a best proximity point for such mappings by considering a new family, which is larger than the family of functions that is often used in fixed-point results for multivalued mappings. To demonstrate the effectiveness of our result, we also give a comparative example to which similar results in the literature cannot be applied. Moreover, we present an application of our main result to homotopic mappings.

On existence results of Volterra-type integral equations via $ C^* $-algebra-valued $ F $-contractions

<abstract><p>It is a fact that $ C^* $-algebra-valued metric space is more general and hence the results in this space are proper improvements of their corresponding ideas in standard metric spaces. With this motivation, this paper focuses on introducing the concepts of $ C^* $-algebra-valued $ F $-contractions and $ C^* $-algebra-valued $ F $-Suzuki contractions and then investigates novel criteria for the existence of fixed points for such mappings. It is observed that the notions examined herein harmonize and refine a number of existing fixed point results in the related literature. A few of these special cases are highlighted and analyzed as some consequences of our main ideas. Nontrivial comparative illustrations are constructed to support the hypotheses and indicate the preeminence of the obtained key concepts. From application viewpoints, one of our results is applied to discuss new conditions for solving a Volterra-type integral equation.</p></abstract>

Towards coupled coincidence theorems of generalized admissible types of mappings on partial satisfactory cone metric spaces and some applications

<abstract><p>This paper introduces a novel class of generalized $ {\alpha} $-admissible contraction types of mappings in the framework of $ {\theta} $-complete partial satisfactory cone metric spaces and proves the existence and uniqueness of coincidence points for such mappings. In this setting, the topology generated and induced by the partial satisfactory cone metric is associated with semi-interior points rather than interior points of the underlying cone. In addition, some applications of the paper's main coincidence point theorems are given. The results of this paper unify, extend and generalize some previously proved theorems in this generalized setting.</p></abstract>

Paired contractive mappings and fixed point results

<abstract><p>In this study, we explored a novel type of contraction, known as paired contraction (PC), to establish fixed points in metric spaces. It has been demonstrated that mappings possessing the PC property are continuous. We have also provided proofs for the existence of fixed points for such mappings with the classical Banach fixed point theorem emerging as a corollary. Furthermore, we presented examples of mappings that do not satisfy the standard contraction condition, but do exhibit the PC property.</p></abstract>

BEST PROXIMITY POINTS OF GENERALIZED p-CYCLIC WEAK φ-CONTRACTIONS

In this manuscript, we extend the notion of generalized cyclic weak φ-contractions to p sets, p ≥ 2. We investigate the convergence of best proximity points of such maps in p-cyclic complete metric spaces. We also give an example to support our main results. Our works generalize and improve the related results in the literature.

On Fixed Points of Enriched Contractions and Enriched Nonexpansive Mappings

We apply the concept of quasilinearization to introduce some enriched classes of Banach contraction mappings and analyse the fixed points of such mappings in the setting of Hadamard spaces. We establish existence and uniqueness of the fixed point of such mappings. To approximate the fixed points, we use an appropriate Krasnoselskij-type scheme for which we establish $\Delta$ and strong convergence theorems. Furthermore, we discuss the fixed points of local enriched contractions and Maia-type enriched contractions in Hadamard spaces setting. In addition, we establish demiclosedness-type property of enriched nonexpansive mappings. Finally, we present some special cases and corresponding fixed point theorems.

Interpolative Prešić Type Contractions and Related Results

In this article, we will extend the notion of interpolative Kannan contraction by introducing the notions of interpolative Prešić type contractions and interpolative Prešić type proximal contractions for mappings defined on product spaces. Through these notions, we will derive some results to ensure the existence of fixed points and best proximity points for such mappings.

Existence, error estimation, rate of convergence, Ulam-Hyers stability, well-posedness and limit shadowing property related to a fixed point problem

In this paper we consider a fixed point problem where the mapping is supposed to satisfy a generalized contractive inequality involving rational terms. We first prove the existence of a fixed point of such mappings. Then we show that the fixed point is unique under some additional assumptions. We investigate four aspects of the problem, namely, error estimation and rate of convergence of the fixed point iteration, Ulam-Hyers stability, well-psoedness and limit shadowing property. In the existence theorem we use an admissibility condition. Two illustration are given. The research is in the line with developing fixed point approaches relevant to applied mathematics.

Strong coupled proximal points of cyclic coupled proximal mappings using Ck-class functions in S-metric spaces

In this paper, we introduce cyclic coupled proximal mapping in S-metric spaces using Ck-class functions and prove the existence of strong coupled proximal points of such mappings in complete S-metric spaces. Also, we provide an example in support of our main result.

Fixed points of generalized $(\varphi,\psi)$)-Jaggi contractions in orbitally complete partially ordered metric spaces

In this paper, we introduce generalized $(\varphi,\psi)$)-Jaggi contraction mappings and prove the existence of fixed points for such mappings in orbitally complete partially ordered metric spaces. We provide examples in support of our results. Our results generalize the results of Harjani, Lopez and Sadarangani \cite{r26harj}.

Alpha- F -Convex Contraction Mappings in b -Metric Space and a Related Fixed Point Theorem

In this paper, we establish fixed point theorems for α - F -convex contraction mappings in b -metric space and prove the existence and uniqueness of fixed points for such mappings. Our result extends and generalizes comparable results in the existing literature. Finally, we provide an example in support of our main finding.