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

Document Type : Research Paper

Authors

1 Institute for Systems Science & KZN e-Skills CoLab‎, ‎Durban University of Technology‎, ‎Durban‎, ‎South Africa

2 School of Mathematics‎, ‎Statistics and Computer Science‎, ‎University of KwaZulu-Natal‎, ‎Durban‎, ‎South Africa‎

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.

Keywords