On coupled generalised Banach and Kannan type contractions

In this paper we have proved two theorems in which we have established the existence of coupled fixed point results in partially ordered complete metric spaces for generalised coupled Banach and Kannan type mappings. The generalisation has been accomplished by following the line of argument given by Geraghty [Proc. Amer. Math. Soc., 40 (1973), 604-608] . Here the mapping are assumed to satisfy certain contractive type inequalities. We have illustrated our result with two examples. First example is presented to show that our result is a proper generalizations of the corresponding results of Bhaskar et al [Nonlinear Anal. TMA, 65 (7) (2006), 1379-1393].