Approximation of solutions of nonlinear equations of hammerstein type in Hilbert space

C. E. Chidume, H. Zegeye

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

Let H be a real Hilbert space. Let F: D(F) ⊆ H 7rarr; H, K: D(K) ⊆ H → H be bounded monotone mappings with R(F) ⊆ D(K), where D(F) and D(K) are closed convex subsets of H satisfying certain conditions. Suppose the equation 0 = u + KFu has a solution in D(F). Then explicit iterative methods are constructed that converge strongly to such a solution. No invertibility assumption is imposed on K, and the operators K and F need not be defined on compact subsets of H.

Original languageEnglish
Pages (from-to)851-858
Number of pages8
JournalProceedings of the American Mathematical Society
Volume133
Issue number3
DOIs
Publication statusPublished - Mar 2005

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Hilbert spaces
Nonlinear equations
Nonlinear Equations
Hilbert space
Monotone Mapping
Subset
Invertibility
Explicit Methods
Approximation
Iterative methods
Converge
Iteration
Closed
Operator

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Approximation of solutions of nonlinear equations of hammerstein type in Hilbert space. / Chidume, C. E.; Zegeye, H.

In: Proceedings of the American Mathematical Society, Vol. 133, No. 3, 03.2005, p. 851-858.

Research output: Contribution to journalArticle

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