A critical remark on ‘‘Fixed point theorems for occasionally weakly compatible mappings | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 21, Issue 2, August 2013, Page 273-275 PDF (300.65 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.1016/j.joems.2013.03.010 | ||||
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| Authors | ||||
| Ravindra K. Bisht* 1; R.P. Pant2 | ||||
| 1Department of Mathematics–Applied Sciences & Humanities, Bipin Tripahti Kumaon Institute of Technology, Dwarahat, 262 553 Almora, Uttarakhand, India | ||||
| 2Department of Mathematics, D.S.B. Campus, Kumaun University, 263 002 Nainital, Uttarakhand, India | ||||
| 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 | ||||
| Fixed point theorems; Occasionally weakly compatible and (E.A.) property | ||||
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