Visco-resolvent algorithms for monotone operators and nonexpansive mappings
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Authors
Peize Li
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.
Shin Min Kang
- Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Korea.
Li-Jun Zhu
- School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China.
Abstract
Two new type of visco-resolvent algorithms for finding a zero of the sum of two monotone operators and a
fixed point of a nonexpansive mapping in a Hilbert space are investigated. The algorithms consist of the
zeros and the fixed points of the considered problems in which one operator is replaced with its resolvent
and a viscosity term is added. Strong convergence of the algorithms are shown. As special cases, we can
approach to the minimum norm common element of the zero of the sum of two monotone operators and the
fixed point of a nonexpansive mapping without using the metric projection. Some applications are included.
Share and Cite
ISRP Style
Peize Li, Shin Min Kang, Li-Jun Zhu, Visco-resolvent algorithms for monotone operators and nonexpansive mappings, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 5, 325--344
AMA Style
Li Peize, Kang Shin Min, Zhu Li-Jun, Visco-resolvent algorithms for monotone operators and nonexpansive mappings. J. Nonlinear Sci. Appl. (2014); 7(5):325--344
Chicago/Turabian Style
Li, Peize, Kang, Shin Min, Zhu, Li-Jun. "Visco-resolvent algorithms for monotone operators and nonexpansive mappings." Journal of Nonlinear Sciences and Applications, 7, no. 5 (2014): 325--344
Keywords
- Monotone operator
- nonexpansive mapping
- zero point
- fixed point
- resolvent.
MSC
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