Taiwanese Journal of Mathematics

Nonlinear Operators of Monotone Type and Convergence Theorems with Equilibrium Problems in Banach Spaces

Wataru Takahashi and Jen-Chih Yao

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Abstract

Our purpose in this paper is first to discuss nonlinear operators and nonlinear projections in Banach spaces which are related to the resolvents of $m$-accretive operators and maximal monotone operators. Some of these operators in Banach spaces are new. Next, we discuss some properties for such nonlinear operators and nonlinear projections in Banach spaces. Further, using these properties, we prove strong convergence theorems by hybrid methods for nonlinear operators with equilibrium problems in Banach spaces.

Article information

Source
Taiwanese J. Math., Volume 15, Number 2 (2011), 787-818.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406235

Digital Object Identifier
doi:10.11650/twjm/1500406235

Mathematical Reviews number (MathSciNet)
MR2810182

Zentralblatt MATH identifier
1248.47050

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
nonlinear mapping fixed point maximal monotone operator accretive operator resolvent duality theorem

Citation

Takahashi, Wataru; Yao, Jen-Chih. Nonlinear Operators of Monotone Type and Convergence Theorems with Equilibrium Problems in Banach Spaces. Taiwanese J. Math. 15 (2011), no. 2, 787--818. doi:10.11650/twjm/1500406235. https://projecteuclid.org/euclid.twjm/1500406235


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