Approximate fixed point sequence for a finite family of asymptotically pseudocontractive mappings

Let EE be a real Banach space and KK be a nonempty, closed, convex, and bounded subset of EE. Let Ti:K→KTi:K→K, i=1,2,…,Ni=1,2,…,N, be NN uniformly LL-Lipschitzian, uniformly asymptotically regular with sequences {εn}{εn}, and asymptotically pseudocontractive mappings with sequences {kn(i)}, where {εn}{εn} and {kn(i)}, i=1,2,…,Ni=1,2,…,N, satisfy certain mild conditions. Let a sequence {xn}{xn} be generated from x1∈Kx1∈K by xn+1≔λnθnx1+[1−λn(1+θn(1+μn))]xn+λnTnnxn+λnθnμnun, for all integers n⩾1n⩾1, where Tn=Tn(modN)Tn=Tn(modN), {un}{un} be a sequence in KK, and {λn}{λn}, {θn}{θn} and {μn}{μn} are three real sequences in [0,1][0,1] satisfying appropriate conditions; then ‖xn−Tlxn‖→0‖xn−Tlxn‖→0 as n→∞n→∞ for each l∈{1,2,…,N}l∈{1,2,…,N}.