Hilbert空间中非扩张余弦族的显式、隐式和黏性迭代

Abstract

Abstract:

In this paper some iterative schemes to approximate a common fixed point of one-parameter nonexpansive cosine family are investigated in Hilbert spaces. By using the theory of cosine families, a series of new convergence theorems are established under some mild conditions for the explicit, implicit and viscosity iteration processes, respectively. Our results show that the above three iterative methods are applicable to the nonexpansive cosine families; and the implicit and viscosity iterations are superior the explicit iteration in convergence.

Key words: Nonexpansive cosine family, Common fixed point, Explicit iteration process, Implicit iteration process, Viscosity iteration process

CLC Number:

47H09

XIAO Jian-Zhong, YAN Jie, ZHU Xing-Hua. Explicit, Implicit and Viscosity Iterations for Nonexpansive Cosine Families in Hilbert Spaces[J].Acta mathematica scientia,Series A, 2014, 34(6): 1518-1531.

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Explicit, Implicit and Viscosity Iterations for Nonexpansive Cosine Families in Hilbert Spaces

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