On generalized {\Phi}-strongly monotone mappings and algorithms for the solution of equations of Hammerstein type

TL;DR

This paper introduces generalized {}-strongly monotone mappings and develops algorithms that ensure strong convergence to solutions of Hammerstein integral equations, extending previous approximation methods.

Contribution

The paper defines a new class of generalized {}-strongly monotone mappings and proposes algorithms with proven convergence for solving Hammerstein equations.

Findings

Established boundedness of auxiliary mappings.

Proved strong convergence of the constructed sequence.

Extended existing results on Hammerstein equation solutions.

Abstract

In this paper, we consider the class of generalized {\Phi}-strongly monotone mappings and the methods of approximating a solution of equations of Hammerstein type. Auxiliary mapping is defined for nonlinear integral equations of Hammerstein type. The auxiliary mapping is the composition of bounded generalized {\Phi}-strongly monotone mappings which satisfy the range condition. Suitable conditions are imposed to obtain the boundedness and to show that the auxiliary mapping is a generalized {\Phi}-strongly which satisfies the range condition. A sequence is constructed and it is shown that it converges strongly to a solution of equations of Hammerstein type. The results in this paper improve and extend some recent corresponding results on the approximation of a solution of equations of Hammerstein type.