Coupled coincidence point theorems for mixed (G, S)-monotone operators on partially ordered metric spaces and applications

Abstract

In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coincidence and coupled common fixed point theorems for such mappings satisfying a nonlinear contraction involving altering distance functions. Presented theorems extend, improve and generalize the very recent results of Harjani, L\'opez and Sadarangani [J. Harjani, B. L\'opez and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Analysis (2010), doi:10.1016/j.na.2010.10.047] and other existing results in the literature. Some applications to periodic boundary value problems are also considered.