A Generalization of Ćirić Fixed Point Theorems

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 (Banach \cite{SB1922}, Kannan \cite{RK1968}, Nadler \cite{SBN1969}, Reich \cite{SR1972}, etc.) Moreover, a multi-valued version for generalized quasi-contraction is also established.