Some random fixed point theorems with PPF dependence for weakly contractive random operator (Q2868071)

A fixed point theorem for weakly contractive maps was proved by \textit{B. E. Rhoades} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 47, No. 4, 2683--2693 (2001; Zbl 1042.47521)], while \textit{I. Beg} and \textit{M. Abbas} [J. Math. Anal. Appl. 315, No. 1, 181--201 (2006; Zbl 1093.47057)] proved a fixed point theorem for random operators satisfying a random weakly contractive condition. In [Differ. Equ. Appl. 4, No. 2, 181--195 (2012; Zbl 1260.47060)], \textit{B. C. Dhage} proved a random fixed point theorem with so-called PPF dependence (i.e., for the operators which may depend on the past, present or future) for contractive random operators and obtained some results on the existence of solutions to random differential equations.NEWLINENEWLINEIn this paper, Rhoades' fixed point theorem for weakly contractive maps, mentioned above, is extended for the random case with PPF dependence and a result for the existence of a random solution with PPF dependence of some type of random equation is obtained.