New results and generalizations for approximate fixed point property and their applications (Q1724437)

Summary: We first introduce the concept of manageable functions and then prove some new existence theorems related to approximate fixed point property for manageable functions and \(\alpha\)-admissible multivalued maps. As applications of our results, some new fixed point theorems which generalize and improve Du's fixed point theorem, Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and Nadler's fixed point theorem and some well-known results in the literature are given.