New coincidence and common fixed point theorems

Abstract

In this paper, we obtain some extensions and a generalization of a remarkable fixed point theorem of Proinov. Indeed, we obtain some coincidence and fixed point theorems for asymptotically regular non-self and self-maps without requiring continuity and relaxing the completeness of the space. Some useful examples and discussions are also given.

Keywords

• Coincidence point
• Fixed point
• Banach contraction
• Quasi-contraction
• Asymptotic regularity