Abstract
In this paper we utilize the concept of manageable functions to define multivalued α⁎-η⁎ manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, and some other well-known results in the literature. Also, we give an illustrating example showing that our results are a proper generalization of Nadler’s theorem and provide an application to integral equations.
Highlights
Introduction and PreliminariesThe Banach contraction principle [1] is an elementary result in metric fixed point theory
We introduce multivalued α∗ − η∗ manageable contraction and prove certain fixed point results
We prove common fixed point theorem for multivalued contraction
Summary
Introduction and PreliminariesThe Banach contraction principle [1] is an elementary result in metric fixed point theory.
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