Abstract
Zero point problems of two accretive operators and fixed point problems of a nonexpansive mappings are investigated based on a Mann-like iterative algorithm. Weak convergence theorems are established in a Banach space.
Highlights
Introduction and preliminaries LetE be a real Banach space and let E∗ be the dual space of E
Given a continuous strictly increasing function: h : R+ → R+, where R+ denotes the set of nonnegative real numbers, such that limr→∞ h(r) = ∞ and h( ) =, we associate with it a generalized duality map Jφ : E → E∗, defined as
We use the generalized duality map associated with the gauge function h(t) = tq– for q >, Jq(x) := x∗ ∈ E∗ : x∗, x = x q, x∗ = x q, ∀x ∈ E
Summary
Introduction and preliminaries LetE be a real Banach space and let E∗ be the dual space of E. We will focus our attention on the problem of finding a common element in Fix(T) ∩ (A + B)– ( ), where T is a nonexpansive mapping, A is an α-inverse strongly accretive operator and B is an maccretive operator, in the framework of uniformly convex and q-uniformly smooth Banach spaces.
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