New fixed point theorems for generalized distances

Abstract

In the recent developments of fixed point theorems is proving the existence of fixed points on partially ordered metric spaces [20, 23], a generalization of the Banach contraction principle for an integral-type inequality [2, 10, 21], and even some applications to matrix equations and ordinary differential equations. In this paper, we want to illustrate some new fixed point theorems for generalized distances with τ -function in the partially ordered metric space rather than w-distance [23]. In short, we would like to utilize τ -function to provide the existence of fixed points on partially ordered metric spaces which is our goal.