Abstract
The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly -Lipschitzian mappings in Banach spaces. The results presented in the paper not only correct some mistakes appeared in the paper by Ofoedu (2006) but also improve and extend some recent results by Chang (2001), Cho et al. (2005), Ofoedu (2006), Schu (1991), and Zeng (2003, 2005).
Highlights
Introduction and preliminariesThroughout this paper, we assume that E is a real Banach space, E∗ is the dual space of E, K is a nonempty closed convex subset of E, and J : E → 2E∗ is the normalized duality mapping defined byJ(x) = f ∈ E∗ : x, f = x 2 = f 2, f = x, x ∈ E, (1.1)where ·, · denotes the duality pairing between E and E∗
The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces
(1) T is said to be uniformly L-Lipschitzian if there exists L > 0 such that for any x, y ∈ K, Tnx − Tn y ≤ L x − y ∀n ≥ 1; (1.2)
Summary
The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper correct some mistakes appeared in the paper by Ofoedu (2006) and improve and extend some recent results by Chang (2001), Cho et al (2005), Ofoedu (2006), Schu (1991), and Zeng (2003, 2005)
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