Approximation of Solutions of Nonlinear Integral Equations of Hammerstein Type. (25th March 2012)

• Record Type: Journal Article
• Authors: Chidume, C. E.; Djitté, N.
• Other Names: Arandiga F. Academic Editor.; Cui J. Academic Editor.
• Is Part Of: ISRN mathematical analysis. Volume 2012(2012)
• Publication Date: 2012-03-25
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Periodicals; 515
• DOI: 10.5402/2012/169751
• Languages: English
• ISSNs: 2090-4657

Abstract

Abstract : Suppose that H is a real Hilbert space and F, K : H → H are bounded monotone maps with D ( K ) = D ( F ) = H . Let u * denote a solution of the Hammerstein equation u + K F u = 0 . An explicit iteration process is shown to converge strongly to u * . No invertibility or continuity assumption is imposed on K and the operator F is not restricted to be angle-bounded. Our result is a significant improvement on the Galerkin method of Brézis and Browder.