Abstract
AbstractLet "Equation missing" be a nonempty compact convex subset of a uniformly convex Banach space "Equation missing", and let "Equation missing" and "Equation missing" be a single-valued nonexpansive mapping and a multivalued nonexpansive mapping, respectively. Assume in addition that "Equation missing" and "Equation missing" for all "Equation missing". We prove that the sequence of the modified Ishikawa iteration method generated from an arbitrary "Equation missing" by "Equation missing", "Equation missing", where "Equation missing" and "Equation missing", "Equation missing" are sequences of positive numbers satisfying "Equation missing", "Equation missing", converges strongly to a common fixed point of "Equation missing" and "Equation missing"; that is, there exists "Equation missing" such that "Equation missing".
Highlights
Let X be a Banach space, and let E be a nonempty subset of X
A mapping t : E → E is said to be nonexpansive if tx − ty ≤ x − y, ∀x, y ∈ E
We introduce an iterative process in a new sense, called the modified Ishikawa iteration method with respect to a pair of single-valued and multivalued nonexpansive mappings
Summary
Let X be a Banach space, and let E be a nonempty subset of X.
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