Global Iterative Schemes for Accretive Operators

C. E. Chidume, H. Zegeye

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Let E be a real q-uniformly smooth Banach space and A:E→2E be an m-accretive operator which satisfies a linear growth condition of the form Ax≤c(1+x) for some constant c0 and for all x∈E. It is proved that if two real sequences {λn} and {θn} satisfy appropriate conditions, the sequence {xn} generated from arbitrary x0∈E by xn+1=xnn(unn(xn-z)); un∈Axnn≥0, converges strongly to some x*∈A-1(0). Furthermore, if E is a reflexive Banach space with a uniformly Gâteaux differentiable norm, and if every weakly compact convex subset of E has the fixed-point property for nonexpansive mappings and A:D(A)E→2E is m-accretive, then for arbitrary, z,x0∈E the sequence {xn} defined by xn+1n(un+1n(x n+1-z))=xn+en, for un∈Axn, where en∈E is such that ∑en<∞∀n≥0, converges strongly to some x*∈A-1(0).

Original languageEnglish
Pages (from-to)364-377
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume257
Issue number2
DOIs
Publication statusPublished - May 15 2001

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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