A generalization of \'Ciri\'c fixed point theorem

TL;DR

This paper extends classical fixed point theorems in metric spaces by introducing a new generalized quasi-contractive map, providing broader conditions for fixed point existence, including multi-valued cases.

Contribution

It presents a novel generalization of Cirić fixed point theorems using a new class of quasi-contractive maps, extending fundamental metrical fixed point results.

Findings

Established a generalized fixed point theorem for single-valued maps.

Developed a multi-valued fixed point theorem for generalized quasi-contractions.

Extended classical fixed point theorems to broader conditions.

Abstract

In this paper, we state and prove a generalization of \'Ciri\'c fixed point theorems in metric space by using a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical fixed point theorems in the literature. Moreover, a multi-valued version for generalized quasi-contraction is also established.