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2013 AN INEXACT PROXIMAL POINT ALGORITHM FOR NONMONOTONE EQUILIBRIUM PROBLEMS IN BANACH SPACES
Guo-ji Tang, Xing Wang
Taiwanese J. Math. 17(6): 2117-2133 (2013). DOI: 10.11650/tjm.17.2013.3266

Abstract

In this paper, we continue to investigate the inexact hybrid proximal point algorithm proposed by Mashreghi and Nasri for equilibrium problems in Banach spaces. Under some classes of generalized monotone conditions, we prove that the sequence generated by the method is strongly convergent to a solution of the problem, which is closest to the initial iterate, in the sense of Bregman distance. As an application, we obtain some analogues for some classes of generalized monotone variational inequalities. The results presented in this paper generalize and improve some recent results in literatures.

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Guo-ji Tang. Xing Wang. "AN INEXACT PROXIMAL POINT ALGORITHM FOR NONMONOTONE EQUILIBRIUM PROBLEMS IN BANACH SPACES." Taiwanese J. Math. 17 (6) 2117 - 2133, 2013. https://doi.org/10.11650/tjm.17.2013.3266

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1305.90387
MathSciNet: MR3141877
Digital Object Identifier: 10.11650/tjm.17.2013.3266

Subjects:
Primary: 47H05 , 90C30

Keywords: Banach space , equilibrium problem , generalized monotonicity , proximal point algorithm , strong convergence , variational inequality

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 6 • 2013
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