Convergence Theorems for a Finite Family of Strictly Asymptotically Pseudocontractive Mappings in Q-Uniformly Smooth Banach Spaces

Abstract:

Let E be a real q-uniformly smooth and uniformly convex Banach space and K a nonempty closed convex subset of E. Let Ti : K ! K, i = 1; 2; : : : ;N be ki-strictly asymptotically pseudocon- tractive mappings with \N i=1F (Ti) 6= ;, where F(Ti) = fx 2 K : Tix = xg. Let fxng be the sequence generated by xn+1 = (1 ¡ ®n)xn + ®nTn [n]xn; where f®ng is a sequence in [0,1] satisfying certain conditions and Tn [n] = Ti n; i = n(modN). Weak and strong convergence theorems for the iterative approximation of common ¯xed points of the family fTigN i=1 are proved.

• Periodical: Applied Mechanics and Materials (Volumes 50-51)
• Pages: 432-436
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.50-51.432
• Online since: February 2011
• Authors: Huan Cheng Zhang, Ai Min Yang, Ya Mian Peng, Jing Guo Qu
• Keywords: Accretive Operator, Common Zeros, Composite Iterative, Resolvent, Uniformly Gateaux Differentiable

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