An over-relaxed (A, η,m)-proximal point algorithm for system of nonlinear fuzzy-set valued operator equation frameworks and fixed point problems

Authors:
Heng-you Lan;Xiao Wang;Tingjian Xiong;Yumin Xiang
Affiliations:
School of Science, Sichuan University of Science & Engineering, Zigong, Sichuan, P.R. China;School of Computer and Science, Sichuan University of Science & Engineering, Zigong, Sichuan, P.R. China;School of Science, Sichuan University of Science & Engineering, Zigong, Sichuan, P.R. China;School of Science, Sichuan University of Science & Engineering, Zigong, Sichuan, P.R. China
Venue:
IUKM'11 Proceedings of the 2011 international conference on Integrated uncertainty in knowledge modelling and decision making
Year:
2011

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Abstract

In order to find the common solutions for nonlinear fuzzy-set valued operator equations and fixed point problems of Lipschitz continuous operators in Hilbert spaces, the purpose of this paper is to construct a new class of over-relaxed (A, η, m)-proximal point algorithm framework with errors by using some results on the resolvent operator corresponding to (A, η, m)-maximal monotonicity. Further, the variational graph convergence analysis for this algorithm framework is investigated. Finally, some examples of applying the main result is also given. The results presented in this paper improve and generalize some well known results in recent literatures.