A note on the paper ‘Fixed point theorems for cyclic weak contractions in compact metric spaces’

Zoran Kadelburg,Stojan Radenović,Jelena Vujaković

doi:10.1186/s13663-016-0537-0

Zoran Kadelburg, Stojan Radenović + Show 1 more

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https://doi.org/10.1186/s13663-016-0537-0

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Abstract

We show that the result on cyclic weak contractions of Harjani et al. (J. Nonlinear Sci. Appl. 6:279-284, 2013) holds without the assumption of compactness of the underlying space, and also without the assumption of continuity of the given mapping.

Highlights

1 Introduction In, Kirk et al introduced in [ ] an interesting concept of cyclic contractions in metric spaces, and obtained the corresponding generalizations of Banach’s, as well as some other fixed point results
Harjani et al [ ] obtained a cyclic fixed point result in compact spaces for weak contractions, modifying a theorem of Karapınar [ ] and Karapınar and Sadarangani [ ]
There are two kinds of fixed point results for cyclic contractions - those assuming that Y = X, and those that do not use this assumption

Summary

Introduction

In , Kirk et al introduced in [ ] an interesting concept of cyclic contractions in metric spaces, and obtained the corresponding generalizations of Banach’s, as well as some other fixed point results. Several authors obtained various fixed point theorems, adapting some other known results to their cyclic variants (see, e.g., [ , – ]). The first results for cyclic contractions in compact metric spaces were obtained already in [ ].

Results

Conclusion