TY - JOUR
T1 - Hybrid approximation of solutions of integral equations of the Hammerstein type
AU - Zegeye, Habtu
AU - Malonza, David M.
N1 - Publisher Copyright:
© 2012, The Author(s).
PY - 2013/6/1
Y1 - 2013/6/1
N2 - Let X be a uniformly convex and uniformly smooth real Banach space with dual X*. Let F : X → X* and K : X* → X be continuous monotone operators. Suppose that the Hammerstein equation u + KFu = 0 has a solution in X. It is proved that a hybrid-type approximation sequence converges strongly to u*, where u* is a solution of the equation u + KFu = 0. In our theorems, the operator K or F need not be defined on a compact subset of X and no invertibility assumption is imposed on K. [Figure not available: see fulltext.]
AB - Let X be a uniformly convex and uniformly smooth real Banach space with dual X*. Let F : X → X* and K : X* → X be continuous monotone operators. Suppose that the Hammerstein equation u + KFu = 0 has a solution in X. It is proved that a hybrid-type approximation sequence converges strongly to u*, where u* is a solution of the equation u + KFu = 0. In our theorems, the operator K or F need not be defined on a compact subset of X and no invertibility assumption is imposed on K. [Figure not available: see fulltext.]
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U2 - 10.1007/s40065-012-0060-z
DO - 10.1007/s40065-012-0060-z
M3 - Article
AN - SCOPUS:85032859354
SN - 2193-5343
VL - 2
SP - 221
EP - 232
JO - Arabian Journal of Mathematics
JF - Arabian Journal of Mathematics
IS - 2
ER -