Abstract
Two new ergodic convergence theorems for approximating the common element of the set of zero points of an m-accretive mapping and the set of fixed points of an infinite family of non-expansive mappings in a real smooth and uniformly convex Banach space are obtained, which improves some of the previous work. The computational experiments to demonstrate the effectiveness of the proposed iterative algorithms in this paper are conducted.
Highlights
Introduction and preliminaries LetE be a real Banach space with norm · and let E∗ denote the dual space of E
We denote the value of f ∈ E∗ at x ∈ E by x, f
T exists for each x, y ∈ {z ∈ E : z = }
Summary
Suppose A : D(A) ⊂ E → E is an m-accretive mapping, where E is a Banach space, and {rn}∞ n= ⊂ ( , +∞) is any real number sequence. For n ≥ , ∀x, y ∈ E, if rn ≤ rn+ , JrAn+ x – JrAn y x–y. ). If rn+ ≤ rn, imitating the proof of
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