Some Simultaneous Generalizations of Well-Known Fixed Point Theorems and Their Applications to Fixed Point Theory

Abstract

In this paper, we first establish a new fixed point theorem that generalizes and unifies a number of well-known fixed point results, including the Banach contraction principle, Kannan’s fixed point theorem, Chatterjea fixed point theorem, Du-Rassias fixed point theorem and many others. The presented results not only unify and generalize the existing results, but also yield several new fixed point theorems, which are different from the well-known results in the literature.

Keywords

• Banach contraction principle
• Kannan’s fixed point theorem
• Chatterjea’s fixed point theorem
• Du–Rassias’s fixed point theorem
• simultaneous generalization
• ℳ?(λ)-function