In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study fixed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

In this article, we prove coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in complete quasi-metric spaces without the mixed g-monotone property, using the concept of invariant condition, together with transitivity with a Qfunction q. We also provide illustrative examples in support of our new results. 2206 Sachin V. Bedre, S. M. Khairnar and B. S. ...

Kaneko and Sessa defined the concept of compatibility for multivalued mappings with Hausdorff metric and proved a coincidence point theorem. After then, Pathak defined the concept of weak compatibility and proved a coincidence theorem. In the present work, we define a new type compatibility for multivalued mappings with Hausdorff metric. This new type compatibility is different from compatibili...

The paper is concerned with a very general version of Caristi’s coincidence theorem, in topological spaces (X, τ) satisfying some completeness conditions with respect to a function p : X ×X → [0,∞), and having as consequence Caristi’s fixed point theorem. The general result is applied to various concrete situations quasi-metric spaces, bornological spaces to obtain versions of Ekeland’s variati...