Strong convergence theorem for approximating zero of accretive operators and application to Hammerstein equation

Olawale Kazeem Oyewole, Matthew Olajiire Aibinu, Lateef Olakunle Jolaoso, Oluwatosin Temitope Mewomo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let C be a nonempty, closed and convex subset of a real q-uniformly smooth Banach space X which admits a weakly sequentially continuous generalized duality mapping jq. We study the approximation of the zero of a strongly accretive operator A: X →X which is also the fixed point of a k strictly pseudo-contractive self mapping on C. We introduce a new algorithm and prove its strong convergence to the zero of A and fixed point of T. The obtained result is applied to the solution of nonlinear integral equation of the Hammerstein type. Our result extends some existing results in literature.

Original languageEnglish
Pages (from-to)23-41
Number of pages19
JournalNonlinear Studies
Volume30
Issue number1
Publication statusPublished - 2023
Externally publishedYes

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