Iterative Solutions of Nonlinear Integral Equations of Hammerstein Type

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Abebe R. Tufa, H. Zegeye, M. Thuto, Iterative Solutions of Nonlinear Integral Equations of Hammerstein Type, Int. J. Anal. Appl., 9 (2) (2015), 129-141.

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Abebe R. Tufa, H. Zegeye, M. Thuto

Abstract

Let H be a real Hilbert space. Let F,K : H → H be Lipschitz monotone mappings with Lipschtiz constants L1and L2, respectively. Suppose that the Hammerstein type equation u + KFu = 0 has a solution in H. It is our purpose in this paper to construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized Hammerstein type equation. The results obtained in this paper improve and extend known results in the literature.

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