A generalized Suzuki Berinde contraction that characterizes Banach spaces

TL;DR

This paper introduces a broad class of contractive mappings called Suzuki Berinde type contractions, establishing fixed point theorems that characterize the completeness of Banach spaces and extending to multivalued mappings.

Contribution

It defines Suzuki Berinde type contractions and proves fixed point theorems that unify and generalize existing results in fixed point theory.

Findings

Suzuki Berinde type contractions always have fixed points.

Fixed point theorems characterize the completeness of normed spaces.

Results extend to multivalued mappings.

Abstract

We introduce a large class of contractive mappings, called Suzuki Berinde type contraction. We show that any Suzuki Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mapping is also obtained. These results unify, generalize and complement various known comparable results in the literature.