Strong and weak convergence theorems for solutions of equations of Hammerstein-type-Reference-Cited by-同舟云学术

Strong and weak convergence theorems for solutions of equations of Hammerstein-type

Published:2023 Issue:2 Volume:37 Page:477-490
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Ofoedu Eric¹,Osigwe Chimezie¹,Ibeh Kingsley¹,Madu Lovelyn²

Affiliation:

1. Department of Mathematics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

2. University of Louisiana, Lafayette, USA; and Department of Mathematics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

Abstract

In this paper, it is our aim in this paper to introduce a new iterative algorithmfor approximation of a solution of an equation of Hammerstein-type. The proposed scheme does not involve computation of inverse of operators under study; it does not involve passing through computation of a certain set that must contain a solution of the equation of Hammerstein-type before convergence takes place. The proposed scheme requires only one parameter satisfying verifiable mild conditions. Moreover, the mappings involved are neither defined on compact subset of the space under study, nor assumed to be angle bounded. Our theorems complement several results that have been obtained in this direction.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference54 articles.

1. H. Brezis and F. E. Browder, Some new results about Hammerstein equations, Bull. Amer. Math. Soc. 80 (1974), 567-572.

2. H. Brezis and F. E. Browder, Existence theorems for nonlinear integral equations of Hamerstein type, Bull. Amer. math. Soc. 81 (1975) 73-78.

3. H. Brezis and F. E. Browder, Nonlinear integral equations and system of Hammerstein type, Advances in math. 18 (1975), 115-147.

4. H. Brezis and F. E. Browder, Singular Hammerstein equations and maximal monotone operators, Bull. Amer. math. Soc. 82 (1976) 623-625.

5. F. E. Browder, Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. Amer. Math. Soc. 73 (1967), 875-882.