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Common fixed point results for two new classes of hybrid pairs in symmetric spaces. (English) Zbl 1225.54018

Summary: Some common fixed point theorems due to M. Abbas and A. R. Khan [Fixed Point Theory Appl. 2009, Article ID 869407, 11 p. (2009; Zbl 1185.54038)], and M. Abbas and B. E. Rhoades [Pan. Amer. Math. J. 18, No. 1, 55–62 (2008; Zbl 1152.54030)] are proved for two new classes of hybrid pairs of mappings which contain occasionally weakly compatible hybrid pairs as a proper subclass. Consequently, some results proved by N. Hussain, M. A. Khamsi and A. Latif [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 6, 2133–2140 (2011; Zbl 1270.47042)], A. Bhatt, H. Chandra and D. R. Sahu [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 1, 176–182 (2010; Zbl 1227.47034)] and many others are extended to hybrid pairs of mappings. Examples are also presented to support the concepts defined in the paper.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
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