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arXiv · 2008.07851

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

M. O. Aibinu·O. T. Mewomo
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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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M. O. Aibinu, O. T. Mewomo. 2020-08-18. On generalized {\Phi}-strongly monotone mappings and algorithms for the solution of equations of Hammerstein type. https://doi.org/10.22075/ijnaa.2019.16797.1894

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