### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Control and Optimization
- Geometry and Topology

### Cite this

*Journal of Nonlinear and Convex Analysis*,

*12*(1), 185-197.

**Fixed point and mean ergodic theorems for new nonlinear mappings in Hilbert spaces.** / Maruyama, Toru; Takahashi, Wataru; Yao, Masayuki.

Research output: Contribution to journal › Article

*Journal of Nonlinear and Convex Analysis*, vol. 12, no. 1, pp. 185-197.

}

TY - JOUR

T1 - Fixed point and mean ergodic theorems for new nonlinear mappings in Hilbert spaces

AU - Maruyama, Toru

AU - Takahashi, Wataru

AU - Yao, Masayuki

PY - 2011/4

Y1 - 2011/4

N2 - 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.

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.

KW - Fixed point

KW - Hilbert space

KW - Hybrid mapping

KW - Mean convergence

KW - Nonexpansive mapping

KW - Nonspreading mapping

UR - http://www.scopus.com/inward/record.url?scp=84655165102&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84655165102&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84655165102

VL - 12

SP - 185

EP - 197

JO - Journal of Nonlinear and Convex Analysis

JF - Journal of Nonlinear and Convex Analysis

SN - 1345-4773

IS - 1

ER -