hybrid steepest-descent method with sequential and functional errors in banach space

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.