School of Mathematics and Computer, Yangtze Normal University, Chongqing, China

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Abstract—In this paper. We introduce a general iterative method for the family of mappings and prove the strong convergence of the new iterative scheme in Banach space. The new iterative method includes the iterative scheme of Khan and Domlo and Fukhar-ud-din [Common fixed points Noor iteration for a finite family of asymptotically quasinonexpansive mappings in Banach spaces. J. Math. Anal. Appl. 341 (2008) 1–11]. The results generalize the corresponding results.

Index Terms—Strong convergence, common fixed point, generalized asymptotically quasi-nonexpansive mapping, viscosity iteration sequence, modified W-mapping.

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Cite: Zhiming Cheng, "Approximation of Common Fixed Points for Families of Mappings in Banach Space," Journal of Computers vol. 7, no. 6, pp. 1467-1473, 2012.