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

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