A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space

作者：Qu De ning; Cheng Cao zong^*

来源：Fixed Point Theory and Applications, 2011, 2011(1): 17.

DOI：10.1186/1687-1812-2011-17

• Common solution
• Equilibrium problem
• Fixed-point problem
• Iterative sequence
• Strong convergence

In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings {A(k)}(k=1)(N) and a system of bifunctions {f(k)}(k=1)(N) satisfying certain conditions, and the common fixed-point problem (P2) for a family of uniformly quasi-phi-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly Holder continuous mappings {S(i)}(i=1)(infinity) are proposed. A new iterative sequence is constructed by using the generalized projection and hybrid method, and a strong convergence theorem is proved on approximating a common solution of (P1) and (P2) in Banach space. 2000 MSC: 26B25, 40A05

• 出版日期2011
• 单位北京工业大学; 吉林师范大学