NEW EXISTENCE THEOREMS FOR APPROXIMATE COINCIDENCE POINT PROPERTY AND APPROXIMATE FIXED POINT PROPERTY WITH APPLICATIONS TO METRIC FIXED POINT THEORY

In this paper, we first establish some new existence theorems concerning approximate coincidence point property and approximate fixed point property for various types of nonlinear contractive maps in metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Kikkawa-Suzuki's fixed point theorem, Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem and some well-known results in the literature. Some applications to the existence of coupled fixed point are also given.