A critical remark on ‘‘Fixed point theorems for occasionally weakly compatible mappings

Document Type : Original Article

Authors

1 Department of Mathematics–Applied Sciences & Humanities, Bipin Tripahti Kumaon Institute of Technology, Dwarahat, 262 553 Almora, Uttarakhand, India

2 Department of Mathematics, D.S.B. Campus, Kumaun University, 263 002 Nainital, Uttarakhand, India

http://dx.doi.org/10.1016/j.joems.2013.03.010

Abstract

In the present paper, we show that under contractive conditions, the existence of a common
fixed point and occasional weak compatibility are equivalent conditions. We also show that
contractive conditions employed by Jungck and Rhoades [Fixed point theorems for occasionally
weakly compatible mappings, Fixed Point Theory 7(2) (2006) 287–296; Fixed Point Theory 9
(2008) 383–384 (erratum)] do not provide a nontrivial setting for the application of occasional weak
compatible mappings. Finally, we improve the results of Jungck and Rhoades by employing a
proper setting.

Keywords

Journal of the Egyptian Mathematical Society
Volume 21, Issue 2 - Serial Number 2
August 2013
Pages 273-275

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