common fixed points for jh-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.