On Some Non-Linear Problems
- 1 January 1968
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 20, 394-397
- https://doi.org/10.4153/cjm-1968-036-1
Abstract
Non-linear problems have been studied by Krasnoselski, Browder, and others; in fact Browder and independently Kirk (cf., 1; 5) have proved the following remarkable theorem: let X be a uniformly convex Banach space, U a non-expansive mapping of a bounded closed convex subset C of X into C, i.e., ||Ux — Uy|| ⩽ ||x — y|| for x, y ∊ C; then U has a fixed point in C. The aim of this paper is to give some existence theorems for non-linear functional equations in uniformly convex Banach spaces. Similar results may be found in (3 ; 6).Keywords
This publication has 0 references indexed in Scilit: