Convergence theorems on an implicit iterative processfor approximating common fixed points of finite strictlypseudocontractive mappings

摘要

Let {T_i}_(i=1)~NbeNstrictly pseudocontractive mappings defined on a non-empty closed convex subset K of a real Banach space E. The implicit iterativescheme X_n=α_nX_(n-1)+β_nT_nx_(n-1)+γ_nT_nX_n,n≥1,where T_n= T_n modN,is introduced to approximate some common fixed points ofthese mappings. Strong and weak convergence theorems are obtained under properconditions. The results presented extend and improve the corresponding results of R.Chen, Y. Song and H. Zhou (J. Math. Anal. Appl. 314:701-709,2006).