Compatible Mappings Research Articles

Common Fixed-Point Theorems for Six Mappings in Symmetric Spaces

In this paper, we establish a common fixed-point theorem for six mappings in symmetric spaces with compatible mapping of type (E) and occasionally weakly compatible mappings. Our work extends the results of Rajopadhyaya et al. [23,25], Aamri and Moutawakil [2] and other similar results in semi-metric space. 2020 Mathematical Sciences Classification: 54H25, 47H10

An Affirmative Result on Banach Space

The aim of this paper is to establish a common fixed point theorem on Banach space using occasionally weakly compatible (OWC) mappings.

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.

Some results on weakly semi compatible mappings in fuzzy metric space

The purpose of this paper is to generate two fixed point theorems in complete fuzzy metric space by using the concepts of weakly semi compatible mappings, sub sequentially continuous mappings and occasionally weakly compatible mappings. Further these results are validated by discussing suitable examples.

COMMON FIXED POINT THEOREMS FOR COMMUTATIVE, WEAKLY COMMUTATIVE AND COMPATIBLE MAPPINGS IN MULTIPLICATIVE CONE METRIC SPACE

n this paper, we introduce the notions of commutative, weakly commutative, and compatible mappings in multiplicative cone metric space and prove common fixed point theorems for these mappings with multiplicative normal cone setting. Also, we give an example to show the validity of our results.

Some coupled coincidence and coupled common fixed point result in dislocated quasi b-metric spaces for rational type contraction mappings

The aim of this paper is to establish coupled coincidence and coupled common fixed point theorems involving a pair of weakly compatible mappings satisfying rational type contractive condition in the setting of dislocated quasi b-metric spaces. The presented result improves and generalizes several well-known comparable results in the existing literature. We also provided an example in support of our main result.

New iterative scheme for fixed point results of weakly compatible maps in multiplicative $ {G_{\boldsymbol{M}}}- $metric space via various contractions with application

<abstract><p>In this manuscript, we induced several vivid common fixed point theorems for four maps in the setting of complete multiplicative $ {G_{\boldsymbol{M}}}- $metric space via various contractive conditions such as $ \Delta $-implicit contractions. Some new definitions and results are introduced in multiplicative $ {G_{\boldsymbol{M}}}- $ metric space.Moreover, illustrative examples are given to validate our obtained results and an application to a system of nonlinear integral equations are provided to show the novelty of our new results.</p></abstract>

Fixed points for weakly compatible mappings

Fixed points for weakly compatible mappings

Common fixed point theorems for occasionally weakly compatible maps satisfying property (E. A) using an inequality involving quadratic terms in manger space for six maps

The purpose of the paper is to establish the existence of two fixed point theorems for six maps under the weaker concept of compatibility called occasionally weakly compatible in Menger space in which the contraction condition contains involving quadratic terms also. The obtained results are improved versions of some of the results obtain in the literature of Fixed Point Theory and Application by employing the property (E. A).

Fixed points for weakly compatible maps with EA and CLR properties

Common fixed point theorems using weakly compatible maps with E.A property as well as common limit range property have been established for the mappings satisfying generalized contraction condition. For the validation of the results an application as well as an example has been given.

Fuzzy Metric Space and Sequel of Common Fixed Point Theorem Using Property E.A.

In the present article, proved a common fixed point theorem in fuzzy metric space using property E.A. for a pair of weakly compatible maps.

Pairs of Compatible Type (B) Mappings and Fixed Point Theory in Banach Space

The present review article is a enhancement of fixed point theorems for two pairs of compatible type (B) mappings with two pairs of weakly compatible mappings in Banach space. The present paper divided into two parts, in first part we have generalized a common fixed point theorem for two pairs of compatible type (B) mappings and in second part we mapped a common fixed point theorem for two pairs of weakly compatible mappings in Banach space using a special type contractive condition usually named square inequality.

COMMON FIXED POINT THEOREM FOR COMPATIBLE MAPPINGS OF TYPE (A-1) IN INTUITIONISTIC MENGER SPACE

The present paper aims to prove some new common fixed point theorems in intutionistic Menger spaces. In this paper some common fixed point results for two pairs of compatible mappings of type (A-1) satisfying contractive condition on intuitionistic menger space are also established. The concept of compatible mappings of type (A-1) was given by Khan et al. [6]. Our results substantially generalize and improve a multitude of relevant common fixed point theorems of the existing literature in metric as well as intutionistic menger spaces.

Weak contraction condition for faintly compatible mappings involving cubic terms of metric functions

In this paper, we obtain a generalized common fixed point theorem for four mappings using the conditions of non-compatibility and faint compatibility satisfying a generalized ∅−weak contraction condition that involves cubic terms of 𝑑(𝑥, 𝑦). Also, we provide an example in support of our result.

Fixed point theorem on partial metric space using weakly compatible and reciprocal continuous mappings

Common fixed point theorem for four self-maps on partial metric spaces by using reciprocally continuous mappings along with compatible and weakly compatible mappings is proved in this paper. We justify the result with an appropriate example.

Some Results of Common Fixed Point for Compatible Mappings in Ƒ-Metric Spaces

Recently, Ƒ-metric space has been started, and a natural topology has been described in these spaces by Jleli and Samet. Furthermore, a new form of the Banach contraction principle has been given in the new spaces. In this work, we present some common fixed-point theorems for two weakly compatible mappings in the Ƒ-metric spaces. We also mention examples that confirm our results.

Deletion and contraction in configuration spaces of graphs

The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and identify the homotopy cofibers in terms of configuration spaces of simpler graphs. The construction's main benefit lies in making the operations functorial - in particular, graph minors give rise to compatible maps at the level of fundamental groups as well as generalized (co)homology theories. As applications we provide a long exact sequence for half-edge deletion in any generalized cohomology theory, compatible with cohomology operations such as the Steenrod and Adams operations, allowing for inductive calculations in this general context. We also show that the generalized homology of unordered configuration spaces is finitely generated as a representation of the opposite graph minor category.

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

Fixed points for weakly compatible mappings

The Common fixed point theorem using weakly compatible maps has been proved that satisfies generalized Ω-weak contraction condition. An application and an example validate our result.

COMMUNAL FIXED POINT IN FUZZY 2- METRIC SPACES

The objective of this paper is to emphasize the Common Fixed Point in Fuzzy 2- Metric Spaces and prove a common fixed point theorem of compatible mappings of type (R) in fuzzy 2-metric space. We consider four mappings of which one is continuous. The results generalize many results in the literature. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and the degree of utility of our results.