Contractive Type Mappings Research Articles

Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings

The fixed point theorems, which are primarily existential in nature, serve as a fundamental topological toolkit for the qualitative analysis of solutions to both linear and nonlinear equations in various branches of mathematics. Many authors have extended and generalized these results in different ways, particularly in the context of fuzzy metric spaces and fuzzy mappings. Numerous researchers have also proved common fixed point theorems under the condition of compatible mappings for fizzy metric spaces. Coupled common fixed point theorems for fuzzy metric spaces with the condition of weakly compatible mappings were attempted to be proved by many authors. Tripled fixed points have emerged as a significant area of research within fixed point theory. Berinde and Borcut introduced the concept of a tripled fixed point for nonlinear mappings in partially ordered metric spaces. They also established a common fixed point theorem for contractive type mappings in M-fuzzy metric spaces. Later, other authors extended these results for common tripled fixed point theorems in fuzzy metric spaces. In this paper we introduce a new technique for proving some new common tripled fixed point theorems for Occasionally Weakly Compatible Mappings in M-fuzzy metric spaces, a method which is not previously utilized by authors in this field. Additionally, we provide illustrative example to support our findings, which represent an improvement over recent results found in the literature.

On Certain Fixed Points for (α,φ,F)-Contraction on S_b- Metric Spaces with Applications

This work establishes unique fixed point theorems (UFPT) for self mapping in complete S_b-metric spaces (S_b-MS) with the concept of (α,φ,F)-contraction in the context of S_b-MS Furthermore, we show how the results may be used and present applications to integral equations and homotopy theory. Introduction: In previous work authors were discussed fixed pointon various metric spaces with F -contractions, α-type almost -F- contractions, α-type F -Suzuki contractions, (φ, F)-contraction, F - weak contractions, α −ψ-contractive type, α −ψ-Meir-Keeler contractive mapping, α-ratonal contractive mappings, (α, β) − (φ,ψ)-rational contractive type mappings. Objectives: Finding the unique fixed point for self mapping in S_b-MS, via (α,φ,F)-contraction. Methods: with the help of α- admisible mapping, (φ, F)-contraction, α type F -contraction and (α.φ,F)-contraction we have fixed point findings in complete S_b-metric spaces. Results: we obtained unique fixed point results via (α,φ,F) contractive type for self mapping in complete S_b-MS. Conclusions: In this article, Contractive mappings of the (α,φ,F) type are used to show certain fixedpoint results in the context of S_b-MS, along with appropriate example that illustrate the key findings. Appications to integral equations and homotopy are also offered.

Some Common Fixed Point Results of Tower Mappings in (Pseudo)modular Metric Spaces

In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results.

Efficient iterative procedures for approximating fixed points of contractive-type mappings with applications

AbstractThis paper introduces and analyzes some new highly efficient iterative procedures for approximating fixed points of contractive-type mappings. The stability, data dependence, strong convergence, and performance of the proposed schemes are addressed. Numerical examples demonstrate that the newly introduced schemes produce approximations of great accuracy and comparable to other similar robust schemes appeared in the literature. Nevertheless, all the schemes developed here are more efficient than other robust schemes used for comparison.

Generalized Twisted (α,β)-ψ Contractive Type Mappings and Related Fixed Point Results with Applications

Generalized Twisted (α,β)-ψ Contractive Type Mappings and Related Fixed Point Results with Applications

On interpolative Hardy-Rogers type cyclic contractions

Recently, Karapınar introduced a new Hardy-Rogers type contractive mapping using the concept of interpolation and proved a fixed point theorem in complete metric space. This new type of mapping, called "interpolative Hardy-Rogers type contractive mapping" is a generalization of Hardy-Rogers's fixed point theorem. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for cyclic mappings on complete metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.

Results in Cone Metric Spaces and Related Fixed Point Theorems for Contractive Type Mappings With Application

In this article, we prove some new fixed point theorems for contractive type mappings in the setting of complete cone metric spaces and provide examples to illustrate the concepts and results developed in the article. We consider some consequences of our results to establish fixed point theorems in the context of cone metric spaces. As an application of our results, periodic point results for the contractive type mappings are proved.

Results in Cone Metric Spaces and Related Fixed Point Theorems for Contractive Type Mappings

The purpose of this article, is to establish some fixed point results for contractive type mappings in cone metric spaces. Examples are provided to support results and concepts presented herein. As an application of our results, we deduce other established fixed point theorems in cone metric spaces.

RATIONAL TYPE INTUITIONISTIC FUZZY CONTRACTION RESULTS IN INTUITIONISTIC FUZZY METRIC SPACES WITH AN APPLICATION

The purpose of this study is to propose a new idea of rational type intuitionistic fuzzy contraction mappings in intuitionistic fuzzy metric spaces. We show several fixed point results in intuitionistic fuzzy metric spaces under rational type intuitionistic fuzzy contraction conditions, with detailed examples to back up our claims. This revolutionary idea will be crucial in the theory of intuitionistic fuzzy fixed point outcomes and can be applied to other contractive type mappings in the setting of intuitionistic fuzzy metric spaces. Furthermore, to support our work, we offer an application of a nonlinear integral type problem to obtain the current result for a unique solution.

Fixed point results for almost ($ \zeta -\theta _{\rho } $)-contractions on quasi metric spaces and an application

<abstract><p>This research paper investigated fixed point results for almost ($ \zeta-\theta _{\rho } $)-contractions in the context of quasi-metric spaces. The study focused on a specific class of ($ \zeta -\theta _{\rho } $)-contractions, which exhibit a more relaxed form of contractive property than classical contractions. The research not only established the existence of fixed points under the almost ($ \zeta -\theta _{\rho } $)-contraction framework but also provided sufficient conditions for the convergence of fixed point sequences. The proposed theorems and proofs contributed to the advancement of the theory of fixed points in quasi-metric spaces, shedding light on the intricate interplay between contraction-type mappings and the underlying space's quasi-metric structure. Furthermore, an application of these results was presented, highlighting the practical significance of the established theory. The application demonstrated how the theory of almost ($ \zeta -\theta _{\rho } $)-contractions in quasi-metric spaces can be utilized to solve real-world problems.</p></abstract>

Some fixed point theorems in fuzzy metric-like spaces

This paper aims to establish some fixed point results for a new class of contractive type mappings in fuzzy metric-like spaces. The results of this paper generalize and extend the Banach contraction principle and some other known results in the setting of fuzzy metric-like spaces.

Generalized Rational Type Contraction and Fixed Point Theorems in Partially Ordered Metric Spaces

In this article, we establish the existence and uniqueness of fixed points for rational type contraction mappings in a metric space that is equipped with a partial order. Our results are shown to improve upon previous results in the literature, and we provide illustrative examples to demonstrate the effectiveness of our approach. Mathematics Subject Classification: 47H10; 54H25.

Comments on the paper ‘A new contribution to best proximity point theory on quasi metric spaces and an application to nonlinear integral equations’

Just recently M. Aslantas [A new contribution to best proximity point theory on quasi metric spaces and an application to nonlinear integral equations. Optimization. 2022] established a new best proximity point theorem multivalued non-self mappings which satisfy an appropriate contractive condition in the framework of quasi metric spaces. Then he applied the existing result to present an application to the solvability of a class of nonlinear integral equations. In this short note, we show that the best proximity point theorem proved in the aforesaid article is a special case of a fixed point theorem for multivalued contraction type mappings which was studied by J. Marin et al. [Q-functions on quasimetric spaces and fixed points for multivalued maps. Fixed Point Theory Appl. 2011:Article ID 603861].

Fixed point on almost generalized (α, ψ, φ, ϑ)-contractive type mappings in weak partial metric spaces

The main objective of this work is to introduce almost generalized (α, ψ, φ, ϑ)-contractive type mappings andinvestigate fixed point theorems for such mappings in weak partial metric spaces. Our results extend and generalize the results of Altun and Durmaz [15] and other existing results in this direction. Moreover, we provide some examples in support of our results.

Fixed point theorems for interpolative $${\grave{\rm C}}{\text{iri}}{\grave{\rm c}}$$-type contraction mappings in convex hull combination of Busemann space with an application to fractional differential equations

Fixed point theorems for interpolative $${\grave{\rm C}}{\text{iri}}{\grave{\rm c}}$$-type contraction mappings in convex hull combination of Busemann space with an application to fractional differential equations

Suzuki type P-contractive mappings

We introduce Suzuki type P-contractive mappings by taking into account the concepts of contractive, P-contractive, and Suzuki type contractive mappings. Then, for such mappings on compact metric spaces, we present a fixed point theorem that is more general than the well-known Edelstein fixed point theorem.

Some applications of fixed point results for monotone multivalued and integral type contractive mappings

The motivation of the present paper is to introduce and establish some new fixed point results for monotone multivalued functions in partially ordered complete D^{*}-metric spaces, where the partial ordered set (X,leq ) is obtained via a pair of functions ( Upsilon,Omega ). Moreover, several existence and uniqueness coupled fixed point theorems of mappings satisfying contractive conditions have been investigated and verified in the setting of partially ordered complete D^{*}-metric spaces by using the concept of integral type contractions with respect to partially ordered D^{*}-metric space. Furthermore, we present appropriate examples as an application for our main results. Our results generalize the work of Ghasab, Majani, and Rad on the study of integral type contraction and coupled fixed point theorems in the ordered G-metric spaces.

The First Rational Type Revised Fuzzy-Contractions in Revised Fuzzy Metric Spaces with an Applications

This paper aims to introduce the concept of rational type revised fuzzy-contraction mappings in revised fuzzy metric spaces. Fixed point results are proven under the rational type revised fuzzy-contraction conditions in revised fuzzy metric spaces with illustrative examples provided to support the results. A significant role will be played by this new concept in the theory of revised fuzzy fixed point results, and it can be generalized for different contractive type mappings in the context of revised fuzzy metric spaces. Additionally, an application of a nonlinear integral type equation is presented to obtain the existing result in a unique solution to support the work.

On Some Fixed Point Iterative Schemes with Strong Convergence and Their Applications

In this paper, a new one-parameter class of fixed point iterative method is proposed to approximate the fixed points of contractive type mappings. The presence of an arbitrary parameter in the proposed family increases its interval of convergence. Further, we also propose new two-step and three-step fixed point iterative schemes. We also discuss the stability, strong convergence and fastness of the proposed methods. Furthermore, numerical experiments are performed to check the applicability of the new methods, and these have been compared with well-known similar existing methods in the literature.

Applying an Extended β-ϕ-Geraghty Contraction for Solving Coupled Ordinary Differential Equations

In this paper, we introduce a new class of mappings called “generalized β-ϕ-Geraghty contraction-type mappings”. We use our new class to formulate and prove some coupled fixed points in the setting of partially ordered metric spaces. Our results generalize and unite several findings known in the literature. We also provide some examples to support and illustrate our theoretical results. Furthermore, we apply our results to discuss the existence and uniqueness of a solution to a coupled ordinary differential equation as an application of our finding.