无限族非扩张非自射映象公共不动点的迭代逼近与Cesàro均值迭代收敛性

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Iterative Approximation to Common |Fixed Points of An Infinite Family of Non-self Non-expansive Maps and Strong Convergence of Cesàro Mean Iterations

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Abstract:

The author introduces and studies an iteration with infinitely many non-expansive nonself mappings in the framework of reflexive and strictly convex Banach spaces. A new strong convergence theorem is obtained, which immediately extends the main result obtained by Zhang-Lee-Chan in 2007 from non-expanive self-mapping to non-expanive non-self-mapping, from Hilbert spaces to Banach spaces. In addition, other main results of this paper extend the main result obtained by R. Wangkeeree in 2007 from Cesàro mean iteration with one non-expansive mapping to Cesàro mean iteration with two ones. Finally, an interesting new result about the set of fixed points of non-expansive mappings is given.

Key words: Sunny non-expansive retraction, Common fixed point, Cesàro mean iterations

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47H09

RAO Ruo-Feng. Iterative Approximation to Common |Fixed Points of An Infinite Family of Non-self Non-expansive Maps and Strong Convergence of Cesàro Mean Iterations[J].Acta mathematica scientia,Series A, 2010, 30(6): 1666-1676.

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