COMMON FIXED POINT FOR RECIPROCALLY CONTINUOUS AND WEAKLY COMPATIBLE MAPS IN A G-METRIC SPACE

Abstract

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.