Approximating solutions of Hammerstein type equations in Banach spaces

O. Daman; Abebe R. Tufa; H. Zegeye

doi:10.2989/16073606.2018.1463299

Approximating solutions of Hammerstein type equations in Banach spaces

O. Daman, Abebe R. Tufa, H. Zegeye

Research output: Contribution to journal › Article › peer-review

Abstract

Let X be a real Banach space and X^∗ be its dual. Let F: X → X^∗ and K: X^∗ → X be Lipschitz monotone mappings. In this paper an explicit iterative scheme is constructed for approximating solutions of the Hammerstein type equation, 0 = u + KF u, when they exist. Strong convergence of the scheme is obtained under appropriate conditions. Our results improve and unify many of the results in the literature.

Original language	English
Pages (from-to)	561-577
Number of pages	17
Journal	Quaestiones Mathematicae
Volume	42
Issue number	5
DOIs	https://doi.org/10.2989/16073606.2018.1463299
Publication status	Published - May 28 2019

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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AB - Let X be a real Banach space and X∗ be its dual. Let F: X → X∗ and K: X∗ → X be Lipschitz monotone mappings. In this paper an explicit iterative scheme is constructed for approximating solutions of the Hammerstein type equation, 0 = u + KF u, when they exist. Strong convergence of the scheme is obtained under appropriate conditions. Our results improve and unify many of the results in the literature.

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Approximating solutions of Hammerstein type equations in Banach spaces

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