A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces

作者：Shehu Yekini^*

来源：Journal of Global Optimization, 2012, 54(3): 519-535.

DOI：10.1007/s10898-011-9775-1

• Relatively nonexpansive mappings
• Generalized projection operator
• Equilibrium problem
• Banach spaces

In this paper, we construct a new iterative scheme and prove strong convergence theorem for approximation of a common fixed point of a countable family of relatively nonexpansive mappings, which is also a solution to an equilibrium problem in a uniformly convex and uniformly smooth real Banach space. We apply our results to approximate fixed point of a nonexpansive mapping, which is also solution to an equilibrium problem in a real Hilbert space and prove strong convergence of general H-monotone mappings in a uniformly convex and uniformly smooth real Banach space. Our results extend many known recent results in the literature.

• 出版日期2012-11