On Almost Contractions in Partially Ordered Metric Spaces <i>via</I> Implicit Relations

Abstract

In this paper, we prove general fixed point theorems for self-maps of a partially ordered complete metric space which satisfy an implicit type relation. Our method relies on constructive arguments involving Picard type iteration processes and our uniqueness result uses comparability arguments. Our results generalize a multitude of fixed point theorems in the literature to the context of partially ordered metric spaces.