WEAK AND STRONG CONVERGENCE THEOREMS FOR GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES

Mayumi Hojo; Wataru Takahashi

doi:10.32219/isms.73.1_31

Scientiae Mathematicae Japonicae

Online ISSN : 1346-0447

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WEAK AND STRONG CONVERGENCE THEOREMS FOR GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES

Mayumi Hojo, Wataru Takahashi

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Keywords: Hilbert space, hybrid mapping, fixed point, mean ergodic theorem, weak convergence, strong convergence

JOURNAL FREE ACCESS

2011 Volume 73 Issue 1 Pages 31-40

DOI https://doi.org/10.32219/isms.73.1_31

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Abstract

In this paper, we first obtain a weak mean convergence theorem of Baillon’s type for generalized hybrid mappings in a Hilbert space. Further, using an idea of mean convergence, we prove a strong convergence theorem of Halpern’s type for generalized hybrid mappings in a Hilbert space.

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