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

    Fingerprint

    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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    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.",
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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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    T1 - Approximation of solutions of nonlinear equations of hammerstein type in Hilbert space

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    AB - 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.

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