Coupled Fixed Point Theorems for Nonlinear Contractions in Partial Metric Spaces

The concept of partial metric which is a generalized metric space was introduced by Matthews 1 in 1994, inwhich the distance between two identical elements needs not be zero. The existence of fixed point for contraction-type mappings on such spaces was considered by many authors 1–12 . A modified version of a Banach contraction mapping principle, more suitable to solve certain problems arising in computer science using the concept of partial metric space is given in 1 . Gnana Bhaskar and Lakshmikantham 13 introduced the concept of coupled fixed point of a mapping F : X×X → X and proved some interesting coupled fixed point theorems for mapping satisfying the mixed monotone property. Later in 14 , Lakshmikantham and Ćirić investigated somemore coupled fixed point theorems in partially ordered sets. For more on coupled fixed point theory, we refer the reader to 2, 14–20 . First, we start by recalling some definitions and properties of partial metric spaces.