Hybrid approximation of solutions of integral equations of the Hammerstein type

Habtu Zegeye, David M. Malonza

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let X be a uniformly convex and uniformly smooth real Banach space with dual X*. Let F : X → X* and K : X* → X be continuous monotone operators. Suppose that the Hammerstein equation u + KFu = 0 has a solution in X. It is proved that a hybrid-type approximation sequence converges strongly to u*, where u* is a solution of the equation u + KFu = 0. In our theorems, the operator K or F need not be defined on a compact subset of X and no invertibility assumption is imposed on K. [Figure not available: see fulltext.]

Original languageEnglish
Pages (from-to)221-232
Number of pages12
JournalArabian Journal of Mathematics
Volume2
Issue number2
DOIs
Publication statusPublished - Jun 1 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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