Nikhilesh Metiya

A generalized weak contraction principle with applications to coupled coincidence point problems

In this paper we establish some coincidence point results for generalized weak contractions with discontinuous control functions. The theorems are proved in metric spaces with a partial order. Our theorems extend several existing results in the current literature. We also discuss several corollaries and give illustrative examples. We apply our result to obtain some coupled coincidence point results which effectively generalize a number of established results.MSC:54H10, 54H25.

Fixed point and common fixed point results in ordered cone metric spaces

Abstract In this paper we establish some fixed point results for functions which satisfy certain weak contractive inequalities in partially ordered cone metric spaces. We have also given some illustrative examples. Our results are extension of some existing

Best Proximity Point Results in Complex Valued Metric Spaces

We introduce the concept of proximity points for nonself-mappings between two subsets of a complex valued metric space which is a recently introduced extension of metric spaces obtained by allowing the metric function to assume values from the field of complex numbers. We apply this concept to obtain the minimum distance between two subsets of the complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces

In this paper, our aim is to ascertain the distance between two sets iteratively in two simultaneous ways with the help of a multivalued coupling define for this purpose. We define the best proximity points of such couplings that realize the distance between two sets. Our main theorem is deduced in metric spaces. As an application, we obtain the corresponding results in uniformly convex Banach spaces using the geometry of the space. We discuss two examples.

EXISTENCE AND STABILITY RESULTS FOR COINCIDENCE POINTS OF NONLINEAR CONTRACTIONS

In this paper we define

End Point Results in Metric Spaces Endowed with a Graph

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

- 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 THEOREMS FOR GENERALIZED WEAKLY CONTRACTIVE MAPPINGS

We introduce the notion of end point of multivalued mappings in the setting of metric space endowed with a graph and prove some existence results in this context. The mappings are assumed to satisfy certain generalized multivalued almost -contractive type inequalities. Further, the consequences of the corresponding results in the cases of single-valued mappings are also discussed with examples.

Coupled coincidence point theorems in ordered metric spaces

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.