TY - JOUR
T1 - Approximating solutions of Hammerstein type equations in Banach spaces
AU - Daman, O.
AU - Tufa, Abebe R.
AU - Zegeye, H.
N1 - Publisher Copyright:
© 2018, © 2018 NISC (Pty) Ltd.
PY - 2019/5/28
Y1 - 2019/5/28
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=85052157887&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85052157887&partnerID=8YFLogxK
U2 - 10.2989/16073606.2018.1463299
DO - 10.2989/16073606.2018.1463299
M3 - Article
AN - SCOPUS:85052157887
SN - 1607-3606
VL - 42
SP - 561
EP - 577
JO - Quaestiones Mathematicae
JF - Quaestiones Mathematicae
IS - 5
ER -