Coupled fixed point theorems for generalized symmetric contractions in partially ordered metric spaces and applications

Abstract

In the setting of partially ordered metric spaces, we introduce the notion of generalized symmetric g-Meir-Keeler type contractions and use the notion to establish the existence and uniqueness of coupled common fixed points. Our notion extends the notion of generalized symmetric Meir-Keeler contractions given by Berinde et. al. [V. Berinde, and M. Pacurar, Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces, Fixed Point Theory and Appl., 2012, 2012:115, doi:10.1186/1687-1812-2012-115] to a pair of mappings. We also give some applications of our main results.