A new best proximity point result with an application to differential inclusions

Abstract

In this paper, we first introduce a new class of contractions via a new concept called a p∗-cyclic contraction mapping, combining the ideas of a cyclic contraction mapping and a p∗-contraction. Then we introduce the definition of a cyclically-complete pair within the context of partial metric spaces. Next, we establish several best proximity point results for p∗-cyclic contraction mappings on D∪E, considering the two cases where (D,E) is a cyclically complete pair and a cyclically 0-complete pair in partial metric spaces. Finally we are investigating the sufficient conditions required to demonstrate the existence of a solution to the differential inclusions using the main result.