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

• Main Authors: Phuengrattana,W., Suantai,S., Wattanawitoon,K., Witthayarat,U., Kumam,P.
• Format: Article
• Published: Eudoxus Press, LLC 2015
• Subjects: Computational Mathematics
• Online Access: http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84911470244&origin=inward; http://cmuir.cmu.ac.th/handle/6653943832/38807
• Institution: Chiang Mai University

© 2014 by Eudoxus Press,LLC,all rights reserved. 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.