A common fixed point theorem for R-weakly commuting mappings in probabilistic spaces with nonlinear contractive conditions

摘要

This paper presents a common fixed point theorem for a family of R-weakly commuting mappings satisfying nonlinear type contractive conditions. This result improves and unifies previous results due to O’Regan and Saadati [D. O’Regan, R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput. 195 (2008) 86–93]. Also, the following results will be probabilistic versions and improvements of the results given in [D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Am. Math. Soc. 20 (1969) 458–464; G. Jungck, Commuting maps and fixed points, Am. Math. Month. 83 (1976) 261–263; R.P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994) 436–440] and many other.