Fixed point and mean ergodic theorems for new nonlinear mappings in Hilbert spaces

Toru Maruyama; Wataru Takahashi; Masayuki Yao

Fixed point and mean ergodic theorems for new nonlinear mappings in Hilbert spaces

Toru Maruyama, Wataru Takahashi, Masayuki Yao

Department of Economic

Research output: Contribution to journal › Article › peer-review

48 Citations (Scopus)

Abstract

In this paper, we first consider a broad class of nonlinear mappings containing the class of generalized hybrid mappings defined by Kocourek, Takahashi and Yao [11] in a Hilbert space. Then, we prove a fixed point theorem, a mean ergodic theorem of Baillon's type [2] and a weak convergence theorem of Mann's type [14] for these nonlinear mappings in a Hilbert space.

Original language	English
Pages (from-to)	185-197
Number of pages	13
Journal	Journal of Nonlinear and Convex Analysis
Volume	12
Issue number	1
Publication status	Published - 2011 Apr 1

Keywords

Fixed point
Hilbert space
Hybrid mapping
Mean convergence
Nonexpansive mapping
Nonspreading mapping

ASJC Scopus subject areas

Analysis
Geometry and Topology
Control and Optimization
Applied Mathematics

Cite this

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AB - In this paper, we first consider a broad class of nonlinear mappings containing the class of generalized hybrid mappings defined by Kocourek, Takahashi and Yao [11] in a Hilbert space. Then, we prove a fixed point theorem, a mean ergodic theorem of Baillon's type [2] and a weak convergence theorem of Mann's type [14] for these nonlinear mappings in a Hilbert space.

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KW - Hilbert space

KW - Hybrid mapping

KW - Mean convergence

KW - Nonexpansive mapping

KW - Nonspreading mapping

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ER -

Fixed point and mean ergodic theorems for new nonlinear mappings in Hilbert spaces

Abstract

Keywords

ASJC Scopus subject areas

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