Let $X$ be a reflexive Banach space, $T:X\to X$ be a nonexpansive mapping with $C=Fix(T)\neq\emptyset$ and $F:X\to X$ 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
