Iterative selection methods for the common fixed point problems in a Banach space

Abstract

Many problems encountered in applied mathematics can be recast as the problem of selecting a particular common fixed point of a countable family of non-expansive mappings in Banach space. In the paper, under the hypotheses that E is a reflexive Banach space which has a weakly continuous duality mapping J φ with gauge function φ, several viscosity approximation methods are investigated for finding a common fixed point of non-expansive mapping sequences.