Equivalence and stability of random fixed point iterative procedures

We generate a sequence of measurable mappings iteratively andstudy necessary conditions for its strong convergence to a randomfixed point of strongly pseudocontractive random operator. Weestablish the weak convergence of an implicit random iterativeprocedure to common random fixed point of a finite family ofnonexpansive random operators in Hilbert spaces. We prove theequivalence between the convergence of random Ishikawa and randomMann iterative schemes for contraction random operator andstrongly pseudocontractive random operator. We also examine thestability of random fixed point iterative procedures for therandom operators satisfying certain contractiveconditions in the context of metric spaces.