One Contractive Inequality onQuasi-normed Space

Abstract

We analyze the existence of fixed points for mappings defined on quasi normed Banach spaces(x,||,-||) satisfying a general contractive inequality of integral type. We are affected from the similar results achieved by A. Branciari and B. E. Rhoades. This condition is extension to Banach-Caccioppolis one. We study mappings f : x for which there exists a real number  c ]0,1[such that for each  x,y Xwe have    where f is a strong measurable mapping which is summable [7],[8, p.1]as well as ||f|| on each compact subset of  and such that for each , . We give a general condition which enables one to easily establish fixed point theorems for a pair of maps satisfying a contractive inequality of integral type.