Hybrid steepest-descent method with sequential and functional errors in Banach space

Document Type : Research Paper


University of Kurdistan


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.


Main Subjects