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

Let XX be a reflexive Banach space, T:XtoXT:XtoX be a nonexpansive mapping with =Fix(T)neqemptysetC=Fix(T)neqemptyset and F:XtoXF:XtoX be deltadelta-strongly accretive and lambdalambda- strictly pseudocotractive with elta+lambda>1delta+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)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.