Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901Hybrid steepest-descent method with sequential and functional errors in Banach space599617230ENS.SaeidiUniversity of KurdistanH.HaydariUniversity of KurdistanJournal Article20100706Let $X$ be a reflexive Banach space, $T:Xto X$ <br />be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto <br />X$ be $delta$-strongly accretive and $lambda$- strictly <br />pseudocotractive with $delta+lambda>1$. In this paper, we present <br /> modified hybrid steepest-descent methods, involving sequential errors and <br />functional errors with functions admitting a center, which generate <br />convergent sequences to the unique solution <br /> of the variational inequality $VI^*(F, C)$. We also present similar results for a strongly monotone and Lipschitzian <br />operator in the context of a Hilbert space and apply the results for <br />solving a minimization problem.http://bims.iranjournals.ir/article_230_c22700f2141e4eab510b5c02df17748f.pdf