%0 Journal Article
%T On generalized $Phi$-strongly monotone mappings and algorithms for the solution of equations of Hammerstein type
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Aibinu, Mathew O.
%A Mewomo, Oluwatosin T.
%D 2021
%\ 02/01/2021
%V 12
%N 1
%P 615-632
%! On generalized $Phi$-strongly monotone mappings and algorithms for the solution of equations of Hammerstein type
%K Generalized ${Phi}$-strongly monotone
%K Hammerstein equation
%K Strong convergence
%R 10.22075/ijnaa.2021.4866
%X 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.
%U https://ijnaa.semnan.ac.ir/article_4866_ad5d2a21a89586ae81e2b41701e58659.pdf