Symmetric Contractions in Partially Ordered Metric Spaces and Coupled Coincidence Points

In this chapter we present new symmetric contractions to produce the existence of coupled coincidence points in the setting of partially ordered metric spaces. The mappings are mixed monotone operators. The contraction considered in our work if of Geraghty type. The main feature of the present chapter is to highlight the fact that the requirements of commutativity or compatibility of the pair of mappings, the monotone hypothesis of mappings involved can be relaxed in coupled coincidence point results which is supported with suitable illustrations.