Abstract

The paper presents some variants to a fixed point theorem of Krasnoselskii for operators on a closed convex subset of a Banach space of the form U + F where U is contractive and F is completely continuous . A study is made of triangle contractive operators in a Hilbert space . It is proved that a triangle contractive operator satisfying certain rather mild conditions is U is contractive and F . is completely continuous Finally , a fixed point theorem is proved for operators of the form U + F where U is triangle contractive and F is completely continuous