Hybrid algorithm for fixed points of Weak relatively nonexpansive mappings and applications

作者：Kang, Jinlong; Su, Yongfu^*; Zhang, Xin

来源：Nonlinear Analysis: Hybrid Systems , 2010, 4(4): 755-765.

DOI：10.1016/j.nahs.2010.05.002

• Weak relatively nonexpansive mapping
• Monotone mapping
• Variational inequality
• Equilibrium problem
• Fixed point

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a weak relatively nonexpansive mapping, the set of solutions of the variational inequality for the monotone mapping and the set of solutions of an equilibrium problem in a 2-uniformly convex and uniformly smooth Banach space. Then we show that the iterative sequence converges strongly to a common element of the three sets. In this paper, we also give an example which is a weak relatively nonexpansive mapping but not a relatively nonexpansive mapping in Banach space l(2).

• 出版日期2010-11
• 单位中国人民解放军国防科学技术大学; 天津工业大学