Abstract
Let E be a real q-uniformly smooth Banach space, which is also uniformly convex (for example, or spaces, ), and C be a nonempty bounded closed convex subset of E. Let be a k-strictly asymptotically pseudocontractive map with a nonempty fixed point set. A hybrid algorithm is constructed to approximate fixed points of such maps. Furthermore, strong convergence of the proposed algorithm is established.
Highlights
Let E be a real Banach space and E* be the dual of E
Where coD denotes the convex closure of the set D, J is the normalized duality mapping, {tn} is a sequence in (, ) with tn →, and PCn∩Dn is the metric projection from E onto Cn ∩ Dn
In this paper, motivated by these facts, we introduce the following iterative algorithm for finding fixed points of a k-strictly asymptotically pseudocontractive mapping T in a uniformly convex and q-uniformly smooth Banach space: x = x ∈ C, C = D = C and
Summary
Let E be a real Banach space and E* be the dual of E. In this paper, motivated by these facts, we introduce the following iterative algorithm for finding fixed points of a k-strictly asymptotically pseudocontractive mapping T in a uniformly convex and q-uniformly smooth Banach space: x = x ∈ C, C = D = C and. ≥ }, where coD denotes the convex closure of the set D, J is the normalized duality mapping, {tn} is a sequence in ( , ) with tn → , and PCn∩Dn is the metric projection from E onto Cn ∩ Dn. The purpose of this paper is to establish a strong convergence theorem of the iterative algorithm [ ] Let E be a real Banach space, C be a nonempty subset of E, and T : C → C be a k-strictly asymptotically pseudocontractive mapping. I – Tn x – I – Tn y q, where L is the uniformly Lipschitzian constant of T and cq > is the constant which appeared in [ , Theorem . ]
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