Simultaneous generalizations of known fixed point theorems for a Meir-Keeler type condition with applications

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.

Keywords:

Simultaneous generalization , Banach's type contraction , Kannan's type contraction , Chatterjea's type contraction , Meir-Keeler's type contraction , Banach contraction principle , Kannan's xed point theorem , Chatterjea's xed point theorem , Meir-Keeler's xed point theorem