Fixed Point and Common Fixed Point Theorems for Cyclic Quasi-Contractions in Metric and Ultrametric Spaces

Parin Chaipunya, Yeol Je Cho, Wutiphol Sintunavarat, Poom Kumam

Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, Korea.
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand.

DOI: 10.4236/apm.2012.26060                

Abstract

In this paper, we prove introduce some fixed point theorems for quasi-contraction under the cyclical conditions. Then, we point out that a common fixed point extension is also applicable via our earlier results equipped together with a weaker cyclical properties, namely a co-cyclic representation. Examples are as well provided along this paper.

Keywords

Cyclic Quasi-Contraction; Co-Cyclic Quasi-Contraction; Metric Space; Ultrametric Space

Conflicts of Interest

The authors declare no conflicts of interest.

References

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