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
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 [ ].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
