Generalization of istratescu's theorem on contractive mappings in metric spaces

Abstract

In this paper we consider mappings T:X→X of metric spaces, satisfying the condition: , where ω is some right semicontinuous function. We prove that if ω is a nondecreasing function, ω(π) 0, π−ω(π)→∞ as π→∞, , then the map T has a fixed point ξ and $$\mathop {\lim }\limits_{n \to \infty } T_x^n = \xi$$ for any pointx∈X. Interesting examples are given.