Abstract

In this paper, we discuss the existence of fixed points for new classes of mappings. Some examples are presented to illustrate our results.

Highlights

  • The Banach contraction principle is one of the most famous and important results in metric fixed point theory

  • It is a useful tool in establishing existence results in nonlinear analysis

  • In [16], the author introduced the class of F-contractions, and established a fixed point result for this class of mappings, which generalizes the Banach contraction principle

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Summary

Introduction

The Banach contraction principle is one of the most famous and important results in metric fixed point theory. In [16], the author introduced the class of F-contractions, and established a fixed point result for this class of mappings, which generalizes the Banach contraction principle. In [5], Ćirić introduced a class of mappings with a non-unique fixed point and he established the following fixed point result. An example was presented in [5] to show that the set of fixed points of mappings satisfying the condition of Theorem 2 contains in general more than one element. A fixed point result is established for this class of mappings. Our fixed point result for this class of mappings has several consequences. For n ∈ N, we denote by T n the nth-iterate of T (we suppose that T 0 is the identity mapping on X)

The Class of Generalized Ćirić-Contractions
A Larger Class of Mappings

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