Coincedence theorem for reciprocally continuous systems of multi-valued and single-valued maps

U C Gairola ,Deepak Khantwal

doi:10.28919/afpt/3544

Abstract

In this paper we eliminate completely the requirement of continuity from the main results of Baillon- Singh [1], Gairola et al. [9] and Gairola-Jangwan [7] and prove a coincidence theorem for systems of single-valued and multi-valued maps on finite product of metric spaces using the concept of coordinatewise reciprocal continuity.

Highlights

In this paper we eliminate completely the requirement of continuity from the main results of BaillonSingh [1], Gairola et al [9] and Gairola-Jangwan [7] and prove a coincidence theorem for systems of single-valued and multi-valued maps on finite product of metric spaces using the concept of coordinatewise reciprocal continuity
Hybrid fixed point theory for nonlinear single-valued and multi-valued maps is a new development within the ambit of multi-valued fixed point theory
Baillon-Singh [1] proved a hybrid fixed point theorem for systems of single-valued and multi-valued maps

Summary

Introduction

Hybrid fixed point theory for nonlinear single-valued and multi-valued maps is a new development within the ambit of multi-valued fixed point theory. In recent formulation, Corley [4] has shown that certain optimization problem are equivalent to a hybrid fixed point theorems. Such theorems appear to be new tools, concerning problems of treatment of images in computer graphics. Singh [1] proved a hybrid fixed point theorem for systems of single-valued and multi-valued maps. Cit.], proved some coincidence theorems for systems of single-valued and multivalued maps by introducing a new class of maps- coordinatewise asymptotically commuting and R-weakly commuting maps. Our result extends and generalizes numerous coincidence and hybrid fixed point results of Czerwik [op. Cit.], Kaneko [14], Kaneko-Sessa [16], Baillon-Singh [op. Our result extends and generalizes numerous coincidence and hybrid fixed point results of Czerwik [op. cit.], Kaneko [14], Kaneko-Sessa [16], Baillon-Singh [op. cit.], Gairola et al [9], Gairola-Jangwan [7] and others

Notations and Definitions

Coincidence Theorem