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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 2/2023

08-10-2022 | Original Research

New iterative methods for finding solutions of Hammerstein equations

Authors: Oganeditse A. Boikanyo, Habtu Zegeye

Published in: Journal of Applied Mathematics and Computing | Issue 2/2023

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Abstract

Let \(G:H\rightarrow H\) and \(K: H\rightarrow H\) be monotone mappings that are either sequentially weakly continuous or continuous, where H is a real Hilbert space. In this work, we introduce two new iterative methods for approximating solutions of the Hammerstein equation \(u+GKu=0\), if they exist. The first iterative method is shown to always converge weakly to an element in the solution set of the Hammerstein equation if this solution set is nonempty. The second iterative method is a modification of the first method to upgrade weak convergence to strong convergence. Convergence results are obtained without requiring the maps to be bounded. Numerical examples are provided to demonstrate the convergence of one of these methods. Comparisons with some existing methods show that the method is cost effective in terms of the number of iterations required to obtain a solution and the computational time.
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Metadata
Title
New iterative methods for finding solutions of Hammerstein equations
Authors
Oganeditse A. Boikanyo
Habtu Zegeye
Publication date
08-10-2022
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 2/2023
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-022-01795-y

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