The modified viscosity implicit rules for uniformly L-Lipschitzian asymptotically pseudocontractive mappings in Banach spaces

The aim of this paper is to establish the modified viscosity implicit rules for uniformly L-Lipschitzian asymptotically pseudocontractive mappings in Banach spaces. The strong convergence theorems of the rules are proved under certain assumptions imposed on the sequences of parameters. As an application, we apply our main results to solve some variational inequalities in Banach spaces, provided T is asymptotically regular. Our results extend the previous known results from Hilbert spaces to Banach spaces and from nonexpansive mappings to asymptotically pseudo-contractive mappings.