Bulletin of the
Korean Mathematical Society BKMS

In this paper, we study the strong convergence and stability of a new two step random iterative scheme with errors for accretive Lipschitzian mapping in real Banach spaces. The new iterative scheme is more acceptable because of much better convergence rate and less restrictions on parameters as compared to random Ishikawa iterative scheme with errors. We support our analytic proofs by providing numerical examples. Applications of random iterative schemes with errors to variational inequality are also given. Our results improve and establish random generalization of results obtained by Chang \cite{4}, Zhang \cite{31} and many others.

Keywords: random iterative schemes, stability, accretive operator, variational inequality

MSC numbers: 47H06, 47H09, 47H10, 47H40, 60H25, 47J25, 49J40