Non-self mappings satisfying non-linear contractive condition with applications

The concept of non-self mappings satisfying a new non-linear contractive type condition is introduced, and coincidence and common fixed point theorems in metric spaces of hyperbolic type are proved. Presented theorems generalize and improve recent theorems of Imdad and Kumar [M. Imdad, S. Kumar, Rhoades-type fixed-point theorems for a pair of nonself mappings, Comput. Math. Appl. 46 (2003), 919–927] and several others theorems. One example is constructed to show that our theorems are genuine generalizations of the above mentioned results of Imdad and Kumar and several others.