Common fixed points for JHJH-operators and occasionally weakly biased pairs under relaxed conditions

Some common fixed point theorems due to 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], Jungck and Rhoades [G. Jungck and B. E. 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)] and Imdad and Soliman [M. Imdad, A.H. Soliman, Some common fixed point theorems for a pair of tangential mappings in symmetric spaces, Appl. Math. Lett. 23 (2010) 351–355] are extended to two new classes of non-commuting selfmaps which contain the occasionally weakly compatible and weakly biased selfmaps as proper subclasses. Some illustrative examples are also provided to highlight the realized improvements.