2010•Journal of Neijiang Normal UniversityRequires access

The CQ Method for Iterative Approximation of Nonexpansive-Mapping Fixed Points in Hilbert Spaces

Zhao Shi-lian

Abstract

By use of CQ method,the Halpern iterative sequences involving nonexpansive mappings have been proven well-defined.Proven also is the sufficient and necessary condition being that such Halpern iterative sequences must be bounded for the existence of fixed points of nonexpansive mappings in the Hilbert spaces.These results can serve to generalize some results of Matsushita and Takahashi.

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Key concepts: Hilbert space, Fixed point, Mathematics, Bounded function, Iterative method, Pure mathematics, Convergence (economics), Applied mathematics