International Journal of Nonlinear Analysis and Applications
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.
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