A coupled common fixed point theorem for a family of mappings

In this paper we introduce the concept of coincidentally commuting pair in the context of coupled fixed point problems. It is established that an arbitrary family of mappings has a coupled common fixed point with two other functions under certain contractive inequality condition where two specific members of the family are assumed to be coincidentally commuting with these two functions respectively. The main result has certain corollaries. An example shows that the main theorem properly contains one of its corollaries

Best proximity point results in set-valued analysis

Here we introduce certain multivalued maps and use them to obtain minimum distance between two closed sets. It is a proximity point problem which is treated here as a problem of finding global optimal solutions of certain fixed point inclusions. It is an application of set-valued analysis. The results we obtain here extend some results and are illustrated with examples. Applications are made to the corresponding single valued cases

Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions

AbstractIn this paper, we establish some fixed point results for mappings involving (ϕ,ψ)-rational type contractions in the framework of metric spaces endowed with a partial order. These results generalize and extend some known results in the literature. Four illustrative examples are given

Existence, uniqueness, Ulam–Hyers–Rassias stability, well-posedness and data dependence property related to a fixed point problem in gamma-complete metric spaces with application to integral equations

In this paper, we study a fixed point problem for certain rational contractions on γ-complete metric spaces. Uniqueness of the fixed point is obtained under additional conditions. The Ulam–Hyers–Rassias stability of the problem is investigated. Well-posedness of the problem and the data dependence property are also explored. There are several corollaries of the main result. Finally, our fixed point theorem is applied to solve a problem of integral equation. There is no continuity assumption on the mapping

Existence, well-posedness of coupled fixed points and application to nonlinear integral equations

We investigate a fixed point problem for coupled Geraghty type contraction in a metric space with a binary relation. The role of the binary relation is to restrict the scope of the contraction to smaller number of ordered pairs. Such possibilities have been explored for different types of contractions in recent times which has led to the emergence of relational fixed point theory. Geraghty type contractions arose in the literatures as a part of research seeking the replacement contraction constants by appropriate functions. Also coupled fixed point problems have evoked much interest in recent times. Combining the above trends we formulate and solve the fixed point problem mentioned above. Further we show that with some additional conditions such solution is unique. Well-posedness of the problem is investigated. An illustrative example is discussed. The consequences of the results are discussed considering α-dominated mappings and graphs on the metric space. Finally we apply our result to show the existence of solution of some system of nonlinear integral equations

EXISTENCE AND STABILITY RESULTS FOR COINCIDENCE POINTS OF NONLINEAR CONTRACTIONS

In this paper we define $\alpha$ - admissibility of multi-valued mapping with respect to a single-valued mapping and use this concept to establish a coincidence point theorem for pairs of nonlinear multi-valued and single-valued mappings under the assumption of an inequality with rational terms. We illustrate the result with an example. In the second part of the paper we prove the stability of the coincidence point sets associated with the pairs of mappings in our coincidence point theorem. For that purpose we define the corresponding stability concepts of coincidence points. The results are primarily in the domain of nonlinear set-valued analysis

Fixed-Point Study of Generalized Rational Type Multivalued Contractive Mappings on Metric Spaces with a Graph

The main result of this paper is a fixed-point theorem for multivalued contractions obtained through an inequality with rational terms. The contraction is an F-type contraction. The results are obtained in a metric space endowed with a graph. The main theorem is supported by illustrative examples. Several results as special cases are obtained by specific choices of the control functions involved in the inequality. The study is broadly in the domain of setvalued analysis. The methodology of the paper is a blending of both graph theoretic and analytic methods.This paper has been supported by the Basque Government though Grant T1207-19

MULTIVALUED FIXED POINT RESULTS AND STABILITY OF FIXED POINT SETS IN METRIC SPACES

In this paper we establish certain multivalued fixed point results for mappings satisfying rational type almost contractions involving a control function in the framework of metric spaces. The main result is supported with an example. We use Hausdorff distance in our theorems. We also study the stability of fixed point sets of above mentioned set valued contractions. By applications of the multivalued results we obtain certain fixed point theorems of singlevalued mappings

Best proximity results for proximal contractions in metric spaces endowed with a graph

In this paper we define a generalized proximal G-contraction on a metric space having the additional structure of a directed graph. We obtain a best proximity point result for such contractions which is with a view to obtaining minimum distance between the domain and range sets. An example illustrating the main theorem is also discussed. The work is in the line of research on mathematical analysis as well as optimization in metric spaces with a graph