S-iterative Process for a Pair of Single Valued and Multi-valued Nonexpansive Mappings
Kritsana Sokhuma, Naknimit Akkasriworn · 2012
Let E be a nonempty compact convex subset of a uniformly convex Banach space X, and t: E → E and T: E → KC(E) be a single valued nonexpansive mapping and a multi-valued nonexpansive map-ping, respectively. Assume in addition that Fix(t) ∩ Fix(T) = ∅ and Tw = {w} for all w ∈ Fix(t) ∩ Fix(T). Suppose {xn} is generated iterative by x1 ∈ E, yn = (1 − βn)xn + βnzn xn+1 = (1 − αn)zn + αntyn, ∀n ≥ 1, where zn ∈ Txn and {αn} , {βn} are sequences of positive numbers satisfying 0 < a ≤ αn, βn ≤ b < 1. Then the sequence {xn} converges strongly to a common fixed point of t and T.