A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces

• Main Authors: Cholamjiak,P., Suantai,S.
• Format: Article
• Published: Springer Netherlands 2015
• Subjects: Control and Optimization; Management Science and Operations Research; Applied Mathematics; Computer Science Applications
• Online Access: http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84865141523&origin=inward; http://cmuir.cmu.ac.th/handle/6653943832/38637
• Institution: Chiang Mai University

We introduce a hybrid method for finding a common element in the solutions set of an equilibrium problem and the common fixed points set of a countable family of relatively quasi-nonexpansive mappings in a Banach space. A strong convergence theorem of the proposed method is established by using the concept of the Mosco convergence when the family {T n} satisfies the (*)-condition. The examples of three generated mappings which satisfy the (*)-condition are also given. Using the obtained result, we give some applications concerning the variational inequality problem and the convex minimization problem. © 2011 Springer Science+Business Media, LLC.