Multivalued ϕ Contractions and Fixed Point Theorems

Abstract

In this paper we establish some fixed point theorems for multivalued
mappings satisfying contractive condition involving gauge function
when the underlying primary structure is $b$-metric space. Our
proposed iterative scheme converges to the the fixed point with
higher order. Moreover, we also calculate priori and posteriori
estimates for the fixed point. Our main results generalize/extend
many per-existing results in literature. Consequently, to
substantiate the validity of our result we obtain the an existence
result for the solution of integral inclusion.