Some Coincidence and Fixed Point Results for Hybrid Contraction

Abstract

Fixed point theory for multi-valued mappings has many useful applications in applied sciences, in particular in Game theory and Mathematical Economics. Thus it is natural to try of extending the known fixed point results for single-valued mappings to the setting of multi-valued mappings. Some theorems of existence of fixed points of single-valued mappings have been extended to the multi-valued case. For example, in 1969 Nadler extended the Banach contraction principle to multi-valued contractive mappings in complete metric space. However, many other questions remain open. Moreover, the study of existence of coincidence and fixed points for hybrid contraction that is a pair of single-valued and multi-valued maps became more interesting due to the recent investigation of Corley in 1986. He gave a good relationship between hybrid fixed points and optimization problems. Here we present the main known results and current research direction in this subject .This talk can be considered as a survey, but some new results are also included.

Mathematics Subject Classifications: 47H10, 54H25.