%0 Journal Article
%T Hybrid steepest-descent method with sequential and functional errors in Banach space
%J Bulletin of the Iranian Mathematical Society
%I Springer and the Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Saeidi, S.
%A Haydari, H.
%D 2013
%\ 09/01/2013
%V 39
%N 4
%P 599-617
%! Hybrid steepest-descent method with sequential and functional errors in Banach space
%K fixed point
%K hybrid steepest-descent method
%K Nonexpansive mapping
%K variational inequality
%R
%X Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences to the unique solution of the variational inequality $VI^*(F, C)$. We also present similar results for a strongly monotone and Lipschitzian operator in the context of a Hilbert space and apply the results for solving a minimization problem.
%U http://bims.iranjournals.ir/article_230_c22700f2141e4eab510b5c02df17748f.pdf