Approximation of Solutions of Nonlinear Equations of Monotone and Hammerstein Type

Robert Gilbert, C. E. Chidume, H. Zegeye

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Let X be a real uniformly smooth and uniformly convex Banach space with dual X *. Let A: X → X * be a bounded uniformly submonotone map. It is proved that a Mann-type approximation sequence converges strongly to Jx * where x * ∈ N(A). Furthermore, as an application of this result an iterative sequence which converges strongly to a solution of the Hammerstein equation u+KFu = 0 is constructed where, F:X→X* and K:X*→X are monotone-type mappings. No invertibility assumption is imposed on K. Moreover, neither K nor F need be compact. Finally, our method is of independent interest.

Original languageEnglish
Pages (from-to)747-758
Number of pages12
JournalInternational Journal of Phytoremediation
Volume82
Issue number8
DOIs
Publication statusPublished - Aug 2003

All Science Journal Classification (ASJC) codes

  • Environmental Chemistry
  • Pollution
  • Plant Science

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