In this paper, the necessary and sufficient conditions for three-step iterative sequences with errors to converge to a common fixed point for three asymptotically quasi-nonexpansive mappings is estab-lished in convex metric spaces. The results of this paper are generaliza-tions and improvements of the corresponding results of Chang [1] -[3], Kim et al. [8], Liu [9] -[11], Ghosh and Debnath [4],
... [Show full abstract] Xu and Noor [15], Shahzad and Udomene [13], Khan and Takahashi [6] and Khan and Ud-din [7]. References [1] S.S. Chang, Some results for asymptotically pseudo-contractive mapping and asymp-totically nonexpansive mappings, Proc. Amer. Math. Soc., Vol. 129, No. 3 (2001), 845-853. [2] S.S. Chang, Iterative approximation problem of fixed points for asymptotically nonex-pansive mappings in Banach spaces, Acta Math. Appl., Vol. 24, No. 2 (2001), 236-241. [3] S.S. Chang, On the approximating problem of fixed points for asymptotically nonex-pansive mappings, Indian J. Pure-ud-din, Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Analysis, Vol. 61 (2005), 1295-1301. 2000 Mathematics Subject Classification. Primary: 41A50; Secondary: 41A65, 47H10. Key words and phrases. Convex metric space, asymptotically quasi-nonexpansive map-ping, asymptotically nonexpansive mapping, three-step iterative sequence with errors, common fixed point.