A hybrid approximation method for equilibrium and fixed point problems for a family of infinitely nonexpansive mappings and a monotone mapping

作者：Cai Gang^*; Hu Chang Song

来源：Nonlinear Analysis: Hybrid Systems , 2009, 3(4): 395-407.

DOI：10.1016/j.nahs.2009.02.007

• Equilibrium problem
• Fixed point
• Nonexpansive mapping
• alpha-inverse-strongly monotone mapping

In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a family of infinitely nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for alpha-inverse-strongly monotone mapping in the framework of a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. Additionally, we utilize our results to study the optimization problem and find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space. Our results improve and extend the results announced by many others.

• 出版日期2009-11
• 单位湖北师范大学