The purpose of  this paper is to study  weak and strong
convergence of a new implicit iteration process to a common fixed
point for a finite family of nonexpansive mappings in a uniformly
convex Banach space. The results obtained in this paper extend and
improve the corresponding results of [C. E. Chidume, N. Shahzad,
Strong convergence of an implicit iteration process for a finite
family of nonexpansive mappings, Nonlinear Anal. 62 (2005)
1149-1156; H.K. Xu, R. Ori, An implicit iterative process for
nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001)
767-773].