Random iterative algorithms and almost sure stability in banach spaces

Many popular iterative algorithms have been used to approximate fixed point of contractive type operators. We define the concept of generalized φ-weakly contractive random operator T on a separable Banach space and establish Bochner integrability of random fixed point and almost sure stability of T with respect to several random Kirk type algorithms. Examples are included to support new results and show their validity. Our work generalizes, improves and provides stochastic version of several earlier results by a number of researchers.