Common fixed point results for two new classes of hybrid pairs in symmetric spaces

Some common fixed point theorems due to Abbas and Khan [M. Abbas, A.R. Khan, Common fixed points of generalized contractive hybrid pairs in symmetric spaces, Fixed Point Theor. Appl. 2009 (2009) 11, Article ID 869407, http://dx.doi.org/10.1155/2009/869407], and Abbas and Rhoades [M. Abbas, B.E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings defined on symmetric spaces, Pan. Amer. Math. J. 18 (1) (2008) 55–62] are proved for two new classes of hybrid pair of mappings which contain occasionally weakly compatible hybrid pairs as a proper subclass. Consequently, some results proved by Hussain et al. [N. Hussain, M.A. Khamsi, A. Latif, Common fixed points for JHJH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Anal. 74 (2011) 2133–2140], Bhatt et al. [A. Bhatt, et al., Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal. 73 (2010) 176–182] and many others are extended to hybrid pair of mappings. Examples are also presented to support the concepts defined in the paper.