Abstract
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. (C) 2010 Elsevier Ltd. All rights reserved.