Taiwanese Journal of Mathematics

TWO GENERALIZED STRONG CONVERGENCE THEOREMS OF HALPERN’S TYPE IN HILBERT SPACES AND APPLICATIONS

Wataru Takahashi, Ngai-Ching Wong, and Jen-Chih Yao

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Abstract

Let $C$ be a closed convex subset of a real Hilbert space $H$. Let $A$ be an inverse-strongly monotone mapping of $C$ into $H$ and let $B$ be a maximal monotone operator on $H$ such that the domain of $B$ is included in $C$. We introduce two iteration schemes of finding a point of $(A+B)^{-1}0$, where $(A+B)^{-1}0$ is the set of zero points of $A+B$. Then, we prove two strong convergence theorems of Halpern's type in a Hilbert space. Using these results, we get new and well-known strong convergence theorems in a Hilbert space.

Article information

Source
Taiwanese J. Math., Volume 16, Number 3 (2012), 1151-1172.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406684

Digital Object Identifier
doi:10.11650/twjm/1500406684

Mathematical Reviews number (MathSciNet)
MR2917261

Zentralblatt MATH identifier
06062770

Subjects
Primary: 47H05: Monotone operators and generalizations 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]

Keywords
maximal monotone operator inverse-strongly monotone mapping zero point fixed point strong convergence theorem equilibrium problem

Citation

Takahashi, Wataru; Wong, Ngai-Ching; Yao, Jen-Chih. TWO GENERALIZED STRONG CONVERGENCE THEOREMS OF HALPERN’S TYPE IN HILBERT SPACES AND APPLICATIONS. Taiwanese J. Math. 16 (2012), no. 3, 1151--1172. doi:10.11650/twjm/1500406684. https://projecteuclid.org/euclid.twjm/1500406684


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