On generalized $\Phi$-strongly monotone mappings and algorithms for the solution of equations of Hammerstein type | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 48، دوره 12، شماره 1، مرداد 2021، صفحه 615-632 اصل مقاله (481.96 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4866 | ||
| نویسندگان | ||
| Mathew O. Aibinu* 1؛ Oluwatosin T. Mewomo2 | ||
| 1Institute for Systems Science & KZN e-Skills CoLab, Durban University of Technology, Durban, South Africa | ||
| 2School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Generalized $\Phi$-strongly monotone؛ Hammerstein equation؛ Strong convergence | ||
| مراجع | ||
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