Summary: T. G. Bhaskar
and V. Lakshmikantham
[Nonlinear Anal., Theory Methods Appl. 65, No. 7, A, 1379–1393 (2006; Zbl 1106.47047
)] proved the existence of a coupled fixed point for a single valued mapping under weak contractive conditions and, as an application, they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, V. Lakshmikantham
and Lj. Ćirić
[Nonlinear Anal., Theory Methods Appl. 70, No. 12, A, 4341–4349 (2009; Zbl 1176.54032
)] obtained a coupled coincidence and coupled common fixed point of two single valued maps. In this article, we extend these concepts to multi-valued mappings and obtain coupled coincidence points and common coupled fixed point theorems involving hybrid pair of single valued and multi-valued maps satisfying generalized contractive conditions in the frame work of a complete metric space. Two examples are presented to support our results.