Coupled Fixed Point Theorems for Partially Contractive Mappings

Abstract

Recently, some authors have started to generalize fixed point theorems for contractive mappings in a class of generalized metric spaces in which the self-distance need not be zero. These spaces, partial metric spaces, were first introduced by Matthews in 1994. The proved fixed point theorems have been obtained for mappings satisfying contraction type conditions empty of the self-distance. In this article, we prove some coupled fixed point theorems for mappings satisfying contractive conditions allowing the appearance of self-distance terms. These partially contractive mappings do reflect the structure of the partial metric space, and hence their coupled fixed theorems generalize the previously obtained by (Aydi in Int. J. Math. Sci. 2011:Article ID 647091, 2011). Some examples are given to support our claims. MSC: 47H10, 54H25.