Unique Common Fixed Point Theorem Research Articles

Some New Rational Contractions Approach to the Solution of Integral Equations via Unique Common Fixed Point Theorems in Complex Valued -Metric Spaces

Some New Rational Contractions Approach to the Solution of Integral Equations via Unique Common Fixed Point Theorems in Complex Valued -Metric Spaces

A Unique Common Fixed Point Theorem for a Metric Space with the Property (E.A)

A Unique Common Fixed Point Theorem for a Metric Space with the Property (E.A)

Interpolative fuzzy Z-contraction with its application to Fredholm non-linear integral equation

The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the existing fuzzy contractions (by Gregori and Sapena [6]), ψ contraction (by Mihet [11]), fuzzy Z-contractions (by Shukla et al. [21]) and Tirado contraction (by Tirado [22]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in [21] through weak compatibility. As an applications, we discuss fixed point theorem for Fredholm non-linear integral equation. The article also includes an example, which shows the validity of our results.

Common fixed point of nonlinear contractive mappings

<abstract><p>The purpose of this paper is to study the existence of a common fixed point for a pair of mappings without assumption of the contractive coefficient being fixed and less than 1. By replacing the fixed contractive coefficient with a nonlinear contractive function, we establish a unique common fixed point theorem for a pair of asymptotically regular self-mappings with either orbital continuity or $ q $-continuity in a metric space. Moreover, by the asymptotical regularity of two approximate mappings, we prove that a pair of nonexpansive and continuous self-mappings, which are defined on a nonempty closed convex subset of a Banach space, have a common fixed point. Some examples are given to illustrate that our results are extensions of a recent result in the existing literature.</p></abstract>

A unique common fixed point for contractive mappings under a new concept

In this paper, we will investigate the existence and uniqueness of common fixed points of certain mappings in the frame of a metric space. The given results cover a number of unique common fixed point theorems especially a result of Phaneendra and Swatmaram [12]. We will also display two examples to illustrate our theorems.

Unique common fixed points in metric-like space

Abstract In this article, two unique common fixed point theorems for four self-maps on a metric-like space by using the concept of occasionally weakly biased maps of type (𝒜) are proved. Our results represent an improvement and extension of some fixed point findings. We justify our results by giving two appropriate examples.

A Focus on Types of Compatible Mappings in \(S\)-metric Space

In this article, we study unique common fixed point theorems for four self mappings in S-metric space using generalized concepts of compatible mappings such as compatible mappings of type (A), type (B) and type (C). Our results are generalizing the theorems proved by Sedghi et al. (Common fixed point of four maps in S-metric spaces, Mathematical Sciences 12 (2018), 137 – 143) in metric space.

A Unique Common Fixed Point under a Weak Altering Distance Function

Abstract In this paper, unique common fixed point theorems for pairs of subcompatible and reciprocally continuous mappings or compatible and subsequentially continuous mappings are obtained. This unique common fixed point is guaranteed under a new concept named a weak altering distance function. Our theorems improve some results especially the ones of [2].

GENERALIZED (ψ, θ, ϕ)-CONTRACTION WITH APPLICATION TO ORDINARY DIFFERENTIAL EQUATIONS

We prove a unique common fixed point theorem and some coupled fixed point results satisfying generalized (ψ, θ, ϕ)-contraction on partially ordered metric spaces. With the help of results established in the first segment, we investigate the solution of periodic boundary value problems as an application. Our results improve, generalize and sharpen various well known results in the literature.

An Approach of Integral Equations in Complex-Valued b -Metric Space Using Commuting Self-Maps

This paper is aimed at establishing some unique common fixed point theorems in complex-valued b -metric space under the rational type contraction conditions for three self-mappings in which the one self-map is continuous. A continuous self-map is commutable with the other two self-mappings. Our results are verified by some suitable examples. Ultimately, our results have been utilized to prove the existing solution to the two Urysohn integral type equations. This application illustrates how complex-valued b -metric space can be used in other types of integral operators.

Outcomes of Common Fixed Point Theorems in S-metric Space

In the present paper, we establish the existence of two unique common fixed point theorems with a new contractive condition for four self-mappings in the S-metric space. First, we establish a common fixed-point theorem by using weaker conditions such as compatible mappings of type-(E) and subsequentially continuous mappings. Further, in the next theorem, we use another set of weaker conditions like sub-compatible and sub-sequentially continuous mappings, which are weaker than occasionally weak compatible mappings. Moreover, it is observed that the mappings in these two theorems are sub-sequentially continuous, but these mappings are neither continuous nor reciprocally continuous mappings. These two results will extend and generalize the existing results of [7] and [9] in the S-metric space. Furthermore, we also provide some suitable examples to justify our outcomes.

Interpolativna uopštena Meir-Kelerova kontrakcija

Introduction/purpose: The aim of this paper is to introduce the notion of an interpolative generalised Meir-Keeler contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the Meir-Keeler contraction which is for only one self map. Using this, we establish a unique common fixed point theorem for two self maps through weak compatibility. The article includes an example, which shows the validity of our results. Methods: Functional analysis methods with a Meir-Keeler contraction. Results: A unique fixed point for self maps in a fuzzy metric space is obtained. Conclusions: A fixed point of the self maps is obtained.

A Result on probabilistic 2-metric space using strong semi compatible mappings

Objective/Aim: To generate a fixed point theorem in probabilistic 2-metric space. Method: By employing strong semi compatible mappings and sub sequentially continuous mappings. Findings: Generated unique common fixed point theorem and substantiated with appropriate example. Novelty/ Improvement: The concepts of strong semi compatible mappings and sub sequentially continuous mappings are weaker than existing conditions like weakly compatible mappings which generalizes the theorem of V. K. Gupta, Arihant Jain and Rajesh kumar. Keywords: Strong semi compatible; sub sequentially continuous; Probabilistic 2metric space; conditional semi compatible; conditional compatible

Some Compatible and Weakly-Compatible Four Self-Mapping Results Approach to Nonlinear Integral Equations in Fuzzy Cone Metric Spaces

This paper is aimed at proving some unique common fixed point theorems by using the compatible and weakly-compatible four self-mappings in fuzzy cone metric (FCM) space. We prove the results under the generalized rational contraction conditions in FCM spaces with the help of one self-map are continuous. Furthermore, we prove some rational contraction results with the weaker condition of the self-mapping continuity. Ultimately, our theoretical work has been utilized to prove the existence solution of the two nonlinear integral equations. This is an illustrative application of how FCM spaces can be used in other integral type operators.

Unique Common Fixed Point Result for Rational Contraction in Complex valued Metric Space

In this paper, we prove some unique common fixed point theorem for two pairs of weakly compatible mappings, satisfying the rational contraction conditions in complex valued metric space. The proved result, generalize and extend some known results in the literature. Finally, The main result is the application of the Urysohn integral equations to derive the existence theorem for a general solution. AMS(MOS) Subject Classification Codes: 47H10, 54H25.

Common Fixed-Point Theorems in the Partial b -Metric Spaces and an Application to the System of Boundary Value Problems

In this paper, we investigate the conditions for the existence of the common fixed points of generalized contractions in the partial b -metric spaces endowed with an arbitrary binary relation. We establish some unique common fixed-point theorems. The obtained results may generalize and improve earlier fixed-point results. We provide examples to illustrate our findings. As an application, we discuss the common solution to the system of boundary value problems.

Fuzzy generalized weak contraction and its application to Fredholm non-linear integral equation in fuzzy metric space

The aim of this paper is to introduce fuzzy generalised weak contractive condition for a pair of self maps in a fuzzy metric space,which is in accordance with the theory of metric spaces given by Rhoades (Nonlinear Analysis 47:2683–2693, 2001). Our results generalize existing fuzzy contraction (by Gregori and Sapena (Fuzzy Sets System 125:245–252, 2002), which is for only one self map. Using this, we establish a unique common fixed point theorem for two self-maps through weak compatibility. The article includes an example, in support of our results. Also an application we established, for the existence and uniqueness of a solution of Fredholm non-linear integral equation in the setting of fuzzy metric space.

Fixed Point Results on Multiplicative Semi-Metric Space


 In this paper we introduce the notion of the Multiplicative Semi-Metric Space and proved common fixed point theorems. We establish fixed point theorems for four self-maps which can be extended to derive common fixed point theorems involving any finite number of mappings in Multiplicative Semi Metric Space. Further examples are discussed to show that compatible mappings of type-E, weakly compatible mappings and reciprocally-continuous mappings are weaker forms of compatible mappings and continuous mappings respectively. The main objective of this article is to prove the unique common fixed point theorems and employing the notion of the compatible mappings of type-E, reciprocally-continuous mappings in the Multiplicative Semi Metric Space. Our result generalizes the concept of Multiplicative Metric Space as it does not involve the multiplicative triangle inequality.

Fixed point theorems for weakly beta-admissible pair of F-contractions with application

In this paper, we introduce a new set Fsb of nonlinear functions. We obtain unique common fixed point theorems for (β; F)-weak contractions under the effect of functions from Fsb. Moreover, we deduce new common fixed point results in ordered and graphic b-metric spaces. Our work generalizes several recent results existing in the literature. We set up an example to elucidate main result. We apply the main theorem to show the existence of common solution of the system of elliptic boundary value problems.

An improvement of known unique common fixed point theorems for four mappings on multiplicative metric spaces

Removing the continuity of four mappings and replacing the compatibility and ϕ-weak commutativity by the weak compatibility, we obtain a generalized result of some well-known unique common fixed point theorems for four mappings defined on multiplicative metric spaces. We also give several deformed common fixed point theorems under non-continuous conditions.