Remarks on occasionally weakly compatible maps versus occasionally weakly compatible maps. (English) Zbl 1331.54048
In the paper under review, the authors discuss some important remarks on the concept of occasionally weakly compatible (owc) mappings. More specifically, they point out the lapses of several authors in quoting the definition of owc mappings and provide the corrected proof by including some additional conditions on their results. Since the corrected versions of the proofs are centered on contractive conditions and now it is well-known that contractive conditions do not provide an ideal setting for the application of the concept of owc mappings [R. P. Pant and R. K. Bisht, Bull. Belg. Math. Soc. - Simon Stevin 19, No. 4, 655–661 (2012; Zbl 1256.54079)]. Therefore, the theorems proved under owc mappings (defined by G. Jungck and B. E. Rhoades [Fixed Point Theory 7, No. 2, 287–296 (2006; Zbl 1118.47045); erratum ibid. 9, No. 1, 383–384 (2008)]) are merely redundant exercises and there is no need of any corrections to those theorems.
Reviewer: Ravindra Kishor Bisht (Gurgaon)
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
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