From the introduction: In 2002, Y. Zhou and S.-S. Chang [Numer. Funct. Anal. Optimization 23, No. 7–8, 911–921 (2002; Zbl 1041.47048)] introduced the following implicit iteration scheme for common fixed points of a finite family of asymptotically nonexpansive mappings in Banach space:
By this implicit iteration scheme, Zhou and Chang proved some weak and strong convergence theorems in Banach spaces for a finite family of nonexpansive mappings.
In this paper, we prove a new convergence theorem of implicit iteration (1) process to a common fixed point for a finite family of total asymptotically pseudocontractive mappings. The results extend those of [S. S. Chang, K. K. Tan, H. W. J. Lee and C. K. Chan, J. Math. Anal. Appl. 313, No. 1, 273–283 (2006; Zbl 1086.47044)].