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

作者：Cholamjiak Prasit; Suantai Suthep^*

来源：Journal of Global Optimization, 2012, 54(1): 83-100.

DOI：10.1007/s10898-011-9743-9

• Common fixed points
• Equilibrium problems
• Mosco convergence
• Relatively quasi-nonexpansive mappings
• Shrinking projection algorithm

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.

• 出版日期2012-9