Fixed Points of Bilateral Multivalued Contractions

Abstract

In this paper, the concepts of Jaggi type bilateral multivalued contractions, Dass - Gupta type bilateral multivalued contraction and Caristi-Ciric type multivalued contraction are introduced in the framework of metric spaces, and we analyze the existence of fixed points for such contractions equipped with some suitable hypotheses. A few consequences in single-valued mappings which include the conclusion of the main result of Chi-Ming et al. [On bilateral contractions. Mathematics, 2019, 7, 538] are obtained. The fact that fixed point of a single-valued mapping satisfying bilateral contractive condition is not necessarily unique, and thereby making the concepts more appropriate for fixed point theorems of multi-valued functions, new multi-valued analogues of the fixed point theorems presented herein are deduced as corollaries. In addition, nontrivial examples is provided to indicate the validity of our results.