Fixed Point Results Research Articles

Fixed Point Results via G-Transitive Binary Relation and Fuzzy L-R-Contraction

In this study, we initiate the concept of fuzzy L-R-contraction and establish some fixed point results involving a G-transitive binary relation and fuzzy L-simulation functions, by employing suitable hypotheses on a fuzzy metric space endowed with a binary relation. The presented results unify, generalize, and improve various previous findings in the literature.

Non-solid cone b-metric spaces over Banach algebras and fixed point results of contractions with vector-valued coefficients

Abstract In this article, without requiring solidness of the underlying cone, a kind of new convergence for sequences in cone b b -metric spaces over Banach algebras and a new kind of completeness for such spaces, namely, wrtn-completeness, are introduced. Under the condition that the cone b b -metric spaces are wrtn-complete and the underlying cones are normal, we establish a common fixed point theorem of contractive conditions with vector-valued coefficients in the non-solid cone b b -metric spaces over Banach algebras, where the coefficients s ≥ 1 s\ge 1 . As consequences, we obtain a number of fixed point theorems of contractions with vector-valued coefficients, especially the versions of Banach contraction principle, Kannan’s and Chatterjea’s fixed point theorems in non-solid cone b b -metric spaces over Banach algebras. Moreover, some valid examples are presented to support our main results.

Certain Fixed Point Results On 𝔄-Metric Space Using Banach Orbital Contraction and Asymptotic Regularity

ABSTRACT In this paper, we investigate the existence of φ-fixed point for Banach orbital contraction over 𝔄-metric space. Also a fixed point result has been established via asymptotic regularity property over such generalized metric space. Our fixed point theorems have also been applied to the fixed circle problem. Moreover, we give some new solutions to the open problem raised by Özgür and Taş on the geometric properties of φ-fixed points of self-mappings and the existence and uniqueness of φ-fixed circles and φ-fixed discs for various classes of self-mappings.

Fixed point results of Jaggi–Suzuki-type hybrid contractions with applications

In this manuscript, a novel general class of contractions, called Jaggi–Suzuki-type hybrid (G-α-ϕ)-contraction, is introduced and some fixed point theorems that cannot be deduced from their akin in metric spaces are proved. The dominance of this family of contractions is that its contractive inequality can be specialized in various manners, depending on multiple parameters. Nontrivial comparative examples are constructed to validate the assumptions of our obtained theorems. Consequently, a number of corollaries that reduce our result to some prominent results in the literature are highlighted and analyzed. Additionally, we examine Ulam-type stability and well-posedness for the new contraction proposed herein. Finally, one of our obtained corollaries is applied to set up unprecedented existence conditions for solution to a class of integral equations. For future aspects of our results, an open problem is noted concerning the discretized population balance model, whose solution may be analyzed using the techniques established herein.

Common Fixed Point Results for Suzuki Type Contractions on Partial Metric Spaces with an Application

In this article, we prove a common fixed point theorem for Suzuki type contractions on complete partial metric spaces. Moreover, we state some corollaries related to Suzuki type common fixed point theorem. And we give an example where we apply our main theorem on complete partial metric spaces. Finally, to show usability of our results, we give its an application showing existence and uniqueness of a common solution for a class of functional equations in dynamic programming.

Fixed Point Results of Rational Type-contraction Mapping in b-Metric Spaces with an Application

In this article, we establish the existence of fixed points of rational type contractions in the setting of b-metric spaces and we verify the T-stability of the P property for some mappings. Also, we present a few examples to illustrate the validity of the results obtained in the paper. Finally, results are applied to find the solution for an integral equation.

Application of Fixed-Point Results to Integral Equation through F-Khan Contraction

In this article, we establish fixed point results by defining the concept of F-Khan contraction of an orthogonal set by modifying the symmetry of usual contractive conditions. We also provide illustrative examples to support our results. The derived results have been applied to find analytical solutions to integral equations. The analytical solutions are verified with numerical simulation.

Fixed-Point Results for (α-ψ)-Fuzzy Contractive Mappings on Fuzzy Double-Controlled Metric Spaces

We introduce the novel concept of (α-ψ)-fuzzy contractive mappings on fuzzy double-controlled metric spaces and demonstrate some fixed-point results. The theorems presented generalize some intriguing findings in the literature. Thus, we prove the fixed-point theorem in the settings of fuzzy double-controlled metric spaces. Furthermore, we provide several examples and an application of our result on the existence of the solution to an integral equation.

Application of Fixed Points in Bipolar Controlled Metric Space to Solve Fractional Differential Equation

Fixed point results and metric fixed point theory play a vital role to find the unique solution to differential and integral equations. Likewise, fractal calculus has vast physical applications. In this article, we introduce the concept of bipolar-controlled metric space and prove fixed point theorems. The derived results expand and extend certain well-known results from the research literature and are supported with a non-trivial example. We have applied the fixed point result to find the analytical solution to the integral equation and fractional differential equation. The analytical solution has been supplemented with numerical simulation.

Relational Contractions Involving (c)-Comparison Functions with Applications to Boundary Value Problems

After the introduction of Alam–Imdad’s relation-theoretic contraction principle, the field of metric fixed point theory has attracted much attention. A number of fixed point theorems in the context of relational metric space employing various types of contractions has been appeared during the last seven years. In this manuscript, one proved a metrical fixed point theorem for ϕ-contraction involving (c)-comparison functions employing an amorphous relation. The result proved in this paper refines, modifies, unifies and sharpens several existing fixed point results. We also constructed an example in order to attest the credibility of our results. Finally, we applied our result to establish the existence and uniqueness of solution of certain periodic boundary value problem.

A Literature Survey on Fixed-Point Results in Metric and Partial Order Metric Spaces

A Literature Survey on Fixed-Point Results in Metric and Partial Order Metric Spaces

Common Fixed Point Results in Bicomplex Valued Metric Spaces with Application

The purpose of this paper is to establish common fixed points of six mappings in the context of bicomplex valued metric spaces. In this way, we generalize some previous well-known results from the literature. Moreover, we provide a non-trivial example to demonstrate the authenticity of established outcomes. As an application, we investigate the solution of an Urysohn integral equation by applying our results.

Fixed Point Results in C🟉-Algebra-Valued Partial b-Metric Spaces with Related Application

In this manuscript, we prove some fixed point theorems on C🟉-algebra-valued partial b-metric spaces by using generalized contraction. We give support and suitable examples of our main results. Moreover, we present a generative application of the main results.

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

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.

A survey of (2+1)-dimensional KdV–mKdV equation using nonlocal Caputo fractal–fractional operator

We analyze the nonlinear (2+1)-dimensional KdV–mKdV equation with Caputo fractal–fractional operator. Some theoretical features are demonstrated via fixed point results. The solution of the considered KdV–mKdV is studied by the composition of the J-transformation and decomposition method. For the validity and effectiveness of the considered method, two examples with suitable initial conditions are solved, where best agreements observed. The validity of the suggested approach is verified by convergence analysis and Picard stability. From the simulations of the obtained results, it is noted that fractional order and fractal dimension significantly affects the amplitude and shape of wave solutions.

Some New Estimates of Fixed Point Results under Multi-Valued Mappings in G-Metric Spaces with Application

It is well known fact that fixed point results are very useful for finding the solution of different types of differential equations. In this paper, some new results of multi-valued functions involving rational inequality in G−metric spaces have been obtained. Some of the new concepts are also defined over G−metric spaces that are open set, interior of set, and limit point of set. Moreover, we have presented the application of our main results in the field of Homotopy. Some non-trivial examples are also provided to discuss the validation of the main finding.

Solving Integral Equations via Hybrid Interpolative ℛℐ-Type Contractions in 𝔟-Metric Spaces

Karapinar et al. established a more general class of contractions, namely, hybrid interpolative Riech Istrǎstescue-type contractions, and presented some results on the platform of metric spaces. This research uses the domain of b-metric spaces to modify this class proficiently. Several interesting fixed-point results are presented by using this new class defined on b-metric space, where the symmetric condition is preserved in this study. Examples are provided for the authentication of proved results. Eventually, an application is also provided in order to comprehend our extensive effort in a better way.

Coincidence Theorems under Generalized Nonlinear Relational Contractions

After the appearance of relation-theoretic contraction principle due to Alam and Imdad, the domain of fixed point theory applied to relational metric spaces has attracted much attention. Existence and uniqueness of fixed/coincidence points satisfying the different types of contractivity conditions in the framework of relational metric space have been studied in recent times. Such results have the great advantage to solve certain types of matrix equations and boundary value problems for ordinary differential equations, integral equations and fractional differential equations. This article is devoted to proving the coincidence and common fixed point theorems for a pair of mappings (T,S) employing relation-theoretic (ϕ,ψ)-contractions in a metric space equipped with a locally finitely T-transitive relation. Our results improve, modify, enrich and unify several existing coincidence points as well as fixed point results. Several examples are provided to substantiate the utility of our results.

Common Fixed Point Results of Suzuki-type Rational Zψ-contractions

In this paper, we combine the (α, β)-admissible mappings and the simulation function in this paper to create the generalized version of Suzuki - type rational Zψ-contraction mapping. This notion is also employed in the setting of metric spaces to get some common fixed point theorems. Appropriate examples are also provided to validate the results acquired.

New Fixed Point Results in Orthogonal B-Metric Spaces with Related Applications

In this article, we present the concept of orthogonal α-almost Istra˘tescu contraction of types D and D* and prove some fixed point theorems on orthogonal b-metric spaces. We also provide an illustrative example to support our theorems. As an application, we establish the existence and uniqueness of the solution of the fractional differential equation and the solution of the integral equation using Elzaki transform.