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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 {\it M. Abbas} and {\it A. R. Khan} [Fixed Point Theory Appl. 2009, Article ID 869407, 11 p. (2009; Zbl 1185.54038)], and {\it M. Abbas} and {\it 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 {\it N. Hussain, M. A. Khamsi} and {\it A. Latif} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 6, 2133--2140 (2011; Zbl 1270.47042)], {\it A. Bhatt, H. Chandra} and {\it 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.

54H25Fixed-point and coincidence theorems in topological spaces
Full Text: DOI
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