Fixed point theorems for contractive and expansive mappings of Geraghty type on 2-metric spaces

Abstract

In this paper, we discuss the unique existence of fixed points for mappings with contractive functions or expansive functions on 2-metric spaces, and give some new versions of the fixed point theorems on real metric spaces. Our results generalize and improve the Banach's contraction principle and some fixed point theorems for expansive mappings on real metric spaces.