Coincidence Point Theorems Research Articles

On Pair of Compatible Mappings and Coincidence Point Theorems in b-Metric Spaces

The main goal of this study is to give two different results for a couple of compatible self-mappings. The first result provides the necessary condition for the existence of a coincidence point for a pair of mappings that are partially weakly increasing in partially ordered b-metric spaces. Additionally, we establish a fixed point result in order to guarantee the uniqueness of common fixed points for pair of maps satisfying the b-(E.A.) Property. Our findings extends and improve well established results of existing literature. In order highlight the distinctiveness of our main theorems, two discrete examples with Tabular and Graphical representations are also presented.

Fixed Point and Coincidence Point Theorems in Dualistic Partial Metric Spaces

In this paper, motivated by Fulga and Proca [1], we define the notion of dualistic E-contraction, generalized dualistic E-contraction, and Dass-Gupta dualistic rational E-contraction. We establish some new fixed-point theorems for E-contraction, generalized dualistic E-contraction, and Dass-Gupta dualistic rational E-contraction in a DPM space. Also, we define dualistic E\(\Delta\) -contraction, generalized dualistic E\(\Delta\)-contraction, and Dass-Gupta dualistic rational E\(\Delta\) -contraction. We establish some common fixed-point theorems for E\(\Delta\) -contraction, generalized dualistic E\(\Delta\)-contraction and Dass-Gupta dualistic rational E\(\Delta\)-contraction in the setting of DPM spaces. Our results extend and generalize some well-known results of [1] and [2]. We also provide an example that shows the usefulness of these contractions.

A brief survey on the development and applications of Goebel’s coincidence point theorem in differential and integral equations

Abstract Goebel’s coincidence theorem, a remarkably simple extension of Banach’s contraction principle widely applied in analysis, has found significant utility in the theory of differential and integral equations. Over the past fifty years, researchers have endeavored to generalize the definition of a metric space, thereby extending the scope of Goebel’s coincidence theorem to diverse settings. This survey paper overviews valuable insights into Goebel’s coincidence theorem’s historical background, its relevance in the field of fixed point theory, and its practical implications in solving problems related to differential and integral equations.

Coincidence point theorems in some generalized metric spaces

"Let (X, d) be a complete dislocated metric space, (Y, ρ) be a semimetric space and f, g : X → Y be two mappings. Several coincidence point results are obtained for singlevalued and multivalued mappings. Keywords: Dislocated metric space, semimetric space, singlevalued and multivalued mapping, comparison function, comparison pair, lower semi-continuity, coincidence point displacement functional, iterative approximation of coincidence point, weakly Picard mapping, pre-weakly Picard mapping."

Exploring Integral ϝ-Contractions with Applications to Integral Equations and Fractional BVPs

In this article, two types of contractive conditions are introduced, namely extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction. For the case of two mappings and their coincidence point theorems, a variant of (ϰ,Ω-Ϝ)-contraction has been introduced, which is called (ϰ,Γ1,2,Ω-Ϝ)-contraction. In the end, the applications of an extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction are given by providing an existence result in the solution of a fractional order multi-point boundary value problem involving the Riemann–Liouville fractional derivative. An interesting existence result for the solution of the nonlinear Fredholm integral equation of the second kind using the (ϰ,Γ1,2,Ω-Ϝ)-contraction has been proven. Herein, an example is established that explains how the Picard–Jungck sequence converges to the solution of the nonlinear integral equation. Examples are given for almost all the main results and some graphs are plotted where required.

Coincidence Point of Edelstein Type Mappings in Fuzzy Metric Spaces and Application to the Stability of Dynamic Markets

In this paper, we prove a coincidence point result for a pair of mappings satisfying Edelstein-type contractive condition on fuzzy metric spaces. We describe the equilibrium of a simple demand–supply model of a dynamic market by the coincidence point of demand and supply functions. With the help of the coincidence point theorem in fuzzy metric spaces, it is showed that a dynamic market of a supply-sensitive nature (or demand-sensitive nature) always tends towards its equilibrium.

Some Coincidence Point Theorems and an Application to Integral Equation in Partially Ordered Metric Spaces

Some Coincidence Point Theorems and an Application to Integral Equation in Partially Ordered Metric Spaces

Fixed and coincidence point theorems on partial metric spaces with an application

The aim of this paper is to investigate some fixed and co-incidence point theorems in complete, orbitally complete and (T, f)-orbitally complete partial metric spaces under the generalized contractive type conditions of mappings. Moreover, our results generalize and extend the several obtained results in the literature. Additionally some non-trivial examples are demonstrated, and an application has discussed to integral equations.

Geometric progressions in distance spaces; applications to fixed points and coincidence points

Conditions on spaces $X$ with generalized distance $\rho_X$ are investigates under which analogues of Banach's and Nadler's fixed-point theorems and Arutyunov's coincidence-point theorem can be obtained for mappings on such spaces. This is shown to hold if each geometric progression with ratio $<1$ (that is, each sequence $\{ x_i\}\subset X$ satisfying $\rho_X(x_{i+1},x_i)\leq \gamma \rho_X(x_i,x_{i-1})$, $ i=1,2,…$, with some $\gamma < 1$) is convergent. Examples of spaces with and without this property are given. In particular, the required property holds in a complete $f$-quasimetric space $X$ if the distance $\rho_X$ in it satisfies $\rho_X(x,z) \leq \rho_X(x,y)+(\rho_X(y,z))^\eta$, $x,y,z \in X$, for some $\eta\in (0,1)$, that is, if the function $f\colon\mathbb{R}_+^{2} \to \mathbb{R}_+$ is given by $f(r_1,r_2)=r_1 + r_2^{\eta}$. Next, for $f(r_1,r_2)=\max\{ r_1^{\eta}, r_2^{\eta} \}$, where $\eta \in (0,2^{-1}]$, it is shown that for any $\gamma > 0$ there exists an $f$-quasimetric space containing a geometric progression with ratio $\gamma$ which is not a Cauchy sequence. The ‘zero-one law’, which means that either each geometric progression with ratio $<1$ is a Cauchy sequence or, for any $\gamma\in (0,1)$, there exists a geometric progression with ratio $\gamma$ that is not Cauchy, is discussed for $f$-quasimetric spaces. Bibliography: 29 titles.

MULTIVALUED COUPLED COINCIDENCE POINT RESULTS IN METRIC SPACES

In this paper, we use an inequality involving a coupled multivalued mapping and a singlevalued mapping to obtain a coupled coincidence point theorem. We discuss special conditions under which coupled common fixed point theorems are obtained. The result combines several ideas prevalent in fixed point theory studies. There are several corollaries and illustrative examples. The Hausdorff-Pompeiu metric between sets is used. The work is in the context of metric spaces and is a part of set-valued analysis with the singlevalued consequences.

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>

Common fixed and coincidence point theorems for nonlinear self-mappings in cone $ b $-metric spaces using $ \varphi $-mapping

<abstract><p>In this paper, by means of a mapping $ \varphi\in\Phi(P, P_1) $, some new common fixed and coincidence point theorems for four and six nonlinear self-mappings in cone $ b $-metric spaces are established, respectively. Also, some examples are given to prove the effectiveness of our results. And with some remarks stating that our results complement and sharply improve some related results in the literature.</p></abstract>

SOME RESULTS IN SOFT COMPACT FUZZY METRIC SPACES AND ITS APPLICATIONS

In this paper we introduced basic notions of soft sets and examined some important properties of soft metric and soft fuzzy metric spaces. The main object of this research article to establish some coincidence point theorems in soft compact fuzzy metric spaces and its applications.

A setvalued coupled coincidence point theorem with data dependence and weak stability results

In this paper, we utilize an inequality involving a coupled multivalued mapping and a singlevalued mapping to obtain a coupled coincidence point theorem. We discuss special conditions under which coupled common fixed point theorems are obtained. The result combines together several ideas prevailing in fixed point theory related studies. There are several corollaries and an illustrative example. In the second part of the paper, we establish a multivalued coupled coincidence point result by putting together several ideas. A contraction through an implicit relation for the coupled mapping is assumed in the main theorem for quadruples of points determined by certain functions. The coupled mapping is also required to satisfy certain dominated conditions which are defined in this paper. In Secs. 3 and 4, we study the data dependence and stability of coupled coincidence point sets, respectively. For describing set distance we use the Hausdorff metric. The work is in the domain of setvalued analysis.

Coupled Fixed Point Theorems with Rational Type Contractive Condition via C-Class Functions and Inverse Ck-Class Functions

The purpose of this paper is to develop coupled fixed point theorems by C-class functions with mixed monotonicity, discuss the existence of the coupled fixed point of two mappings and obtain a coupled coincidence point theorem via inverse Ck-class functions in partially ordered H-metric spaces. This improves the existing results. In addition, some instances and an application are given to illustrate the usability and validity of the results.

Inverse of Berge’s maximum theorem in locally convex topological vector spaces and its applications

Abstract In this paper, the inverse of Berge’s maximum theorem is established in a locally convex topological vector space. Using this result, the generalized Gale–Nikaido–Debreu’s lemma and the generalized coincidence point theorem are derived from the equilibrium theorem of generalized games. By combining the inverse of Berge’s maximum theorem with the generalized coincidence point theorem, the equilibrium theorem of the generalized game is obtained immediately. Finally, we show that Fan–Glicksberg’s fixed point theorem and von Neumann’s lemma can be derived directly from the coincidence point theorem.

SOME COINCIDENCE POINT THEOREMS IN MODULAR SPACES

In metric spaces, there are quasi-contraction mappings and Suzuki-contraction mapping, that are generalization of contraction mappings. In this article, we give coincidence point theorems of quasi-contraction mappings and Suzuki-contraction mappings in modular spaces, that are generalizations of fixed point theorem of quasi-contractraction mappings and Suzuki-contraction theorem in modular spaces.

Upper semicontinuous selections for fuzzy mappings in noncompact $ WPH $-spaces with applications

<abstract><p>In this paper, we introduce the concept of a $ WPH $-space without linear structure and proceed to establish a new upper semicontinuous selection theorem for fuzzy mappings in the framework of noncompact $ WPH $-spaces as well as a special form of this selection theorem in crisp settings. As applications, fuzzy collective coincidence point theorems, fuzzy collectively fixed point theorems, and existence theorems of equilibria for the generalized fuzzy games with three constraint set-valued mappings and generalized fuzzy qualitative games in $ WPH $-spaces are obtained. As their special cases in crisp settings, we derive existence theorems of equilibria for generalized games and generalized qualitative games. Finally, we construct a multiobjective game model for water resource allocation and prove the existence of Pareto equilibria for this multiobjective game based on the existence theorem of equilibria for qualitative games.</p></abstract>

Edge Theoretic Extended Contractions and Their Applications

Edge theoretic extended contractions are introduced and coincidence point theorems and common fixed-point theorems are proved for such contraction mappings in a metric space endowed with a graph. As further applications, we have proved the existence of a solution of a nonlinear integral equation of Volterra type and given a suitable example in support of our result.

Application of Some Fixed-Point Theorems in Orthogonal Extended S-Metric Spaces

In this study, we obtain some coincidence point theorems for weakly O - α -admissible contractive mappings in an orthogonal extended S -metric space. An example and an application are provided to illustrate the usability of the obtained results. Our results generalize the results of several studies from metric and S -metric frameworks to the setting of orthogonal extended S -metric spaces.