Common Fixed Points Approximation for Asymptotically Nonexpansive Semigroup in Banach Spaces

Abstract

Let be a real Banach space satisfying local uniform Opial's condition, whose duality map is weakly sequentially continuous. Let be a uniformly asymptotically regular family of asymptotically nonexpansive semigroup of with function . Let and be weakly contractive map. Let be -strongly accretive and -strictly pseudocontractive map with . Let be an increasing sequence in and let and be sequences in satisfying some conditions. For some positive real number appropriately chosen, let be a sequence defined by , ,  ,  . It is proved that converges strongly to a common fixed point of the family which is also the unique solution of the variational inequality .