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

Bisht, Ravindra K.; Pant, R.P.

doi:10.1016/j.joems.2013.03.010

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

Document Type : Original Article

Authors

Ravindra K. Bisht ¹
R.P. Pant ²

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

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