Fixed points on 2-metric spaces

Abstract

The concept of a 2-metric space was introduced by S. Gabler [3], Recently the 2-metric spaces has been developed extensively in different subjects by others, for example [5], [6] and [7]. Definition 1.1. Let F be a function from a non-empty set X into itself such that Fx = x. Then x in X is called a fixed point of F. Definition 1.2. A 2-metric space is a space X in which for each triple points x, y, z there exists with a real function d defined on XxXxX such that (i) to each pair of points x, y with xy from X, there is zey such that d(x, y, z) 0.