An Iterative Algorithm for Approximating Solutions of Hammerstein Equations with Bounded Generalized Phi-Monotone Mappings. (11th March 2020)

• Record Type: Journal Article
• Authors: Chidume, C. E.; Bello, A. U.
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 4(2020)
• Page Start: 442
• Page End: 461
• Publication Date: 2020-03-11
• Subjects: Bounded Φi-strongly monotone mappings -- Hammerstein equations -- strong convergence; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1659815
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Let E = L p, 1 < p < ∞ and E * denote its dual space. Let F : E → E * and K : E * → E be bounded generalized Φ 1 -strongly, and Φ 2 -strongly monotone maps, respectively. Suppose the Hammerstein equation u + K F u = 0 has a solution u * in E . An iteration sequence is constructed and proved to converge strongly to u *. Our technique of proof is also of independent interest.