Convergence theorems for -expansive and accretive mappings

✍ Scribed by Habtu Zegeye; Naseer Shahzad

• Book ID: 103845957
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 189 KB
• Volume: 66
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2005.11.011

✦ Synopsis

Let E be a real Banach space, and let A : D(A) ⊆ E → E be a Lipschitz, ψ-expansive and accretive mapping such that co(D(A)) ⊆ ∩ λ>0 R(I + λA). Suppose that there exists x 0 ∈ D(A), where one of the following holds: (i) There exists R > 0 such that ψ(R) > 2 A(x 0 ) ; or (ii) There exists a bounded neighborhood U of x 0 such that t (xx 0 ) ∈ Ax for x ∈ ∂U ∩ D(A) and t < 0. An iterative sequence {x n } is constructed to converge strongly to a zero of A. Related results deal with the strong convergence of this iteration process to fixed points of ψ-expansive and pseudocontractive mappings in real Banach spaces. The convergence results established in this paper are new for this more general class of ψ-expansive and accretive or pseudocontractive mappings.