Iterative solution of nonlinear equations of accretive and pseudocontractive types

C. E. Chidume, Hab Zegeye

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Let E be a real uniformly smooth Banach space. Let A: D(A) = E → 2E be an accretive operator that satisfies the range condition and A-1(0) ≠. Let {λn} and {θn} be two real sequences satisfying appropriate conditions, and for z ∈ E arbitrary, let the sequence {xn} be generated from arbitrary x0 ∈ E by xn+1 = xn - λn (un + θn(xn - z)), un ∈ Axn, ≥ 0. Assume that {un} is bounded. It is proved that {xn} converges strongly to Some x* ∈ A-1 (0). Furthermore, if K is a nonempty closed convex subset of E and T: K → K is a bounded continuous pseudocontractive map with F (T) := {Tx = x} ≠, it is proved that for arbitrary z ∈ K, the sequence {xn} generated from x0 ∈ K by xn+1 = xn - λn ((I - T)xn + θn (xn - z)), n ≥ 0,) where {λn} and {θn} are real sequences satisfying appropriate conditions, converges strongly to a fixed point of T.

Original languageEnglish
Pages (from-to)756-765
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume282
Issue number2
DOIs
Publication statusPublished - Jun 15 2003

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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