Weak and strong convergence theorems of proximal point algorithm for solving generalized mixed equilibrium problems and finding zeroes of maximal monotone operators in banach spaces
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Author list: Phuengrattana W., Suantai S., Wattanawitoon K., Witthayarat U., Kumam P.
Publisher: Eudoxus Press LLC
Publication year: 2014
Journal: Journal of Computational Analysis and Applications (1521-1398)
Volume number: 16
Issue number: 2
Start page: 264
End page: 281
Number of pages: 18
ISSN: 1521-1398
Languages: English-Great Britain (EN-GB)
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Abstract
Based on the results proposed by Li and Song [Modified proximal-point algorithm for maximal monotone operators in Banach spaces], J. Optim. Theory appl. 138 (2008) 45-64.], we modify and generate our new iterative scheme for solving generalized mixed equilibrium problems and finding zeroes of maximal monotone operators in a Banach space under the appropriate conditions. We also prove strong and weak convergence theorems of this proximal point algorithm and give an example with numerical test which corresponding to our main results. Furthermore, we also consider the convex minimization problem and the problem of finding a zero point of an α-inverse strongly monotone operator as its appplications. © 2014 by Eudoxus Press,LLC,all rights reserved.
Keywords
Generalized mixed equilibrium problems, Maximal monotone operators, Proximal point algorithm, Weak convergence
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