A TOPOLOGY IN A VECTOR LATTICE AND FIXED POINT THEOREMS FOR NONEXPANSIVE MAPPINGS - Kawasaki, T. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
In the previous paper [4] we show Takahashi’s and Fan-Browder’s fixed point theorems in a vector lattice and in the previous paper [5] we show Schauder-Tychonoff’s fixed point theorem using Fan-Browder’s fixed point theorem. The purpose of this paper is to introduce a topology in a vector lattice and to show a fixed point theorem for a nonexpansive mapping and also common fixed point theorems for commutative family of nonexpansive mappings in a vector lattice.