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

• Main Authors: Qu De-ning, Cheng Cao-zong
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Fixed Point Theory and Applications
• Subjects: Common solution; Equilibrium problem; Fixed-point problem; Iterative sequence; Strong convergence
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2011/1/17
• ISSN: 1687-1820; 1687-1812

<p>Abstract</p> <p>In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings <inline-formula><graphic file="1687-1812-2011-17-i1.gif"/></inline-formula> and a system of bifunctions <inline-formula><graphic file="1687-1812-2011-17-i2.gif"/></inline-formula> satisfying certain conditions, and the common fixed-point problem (P2) for a family of uniformly quasi-<it>&#981;</it>-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly H&#246;lder continuous mappings <inline-formula><graphic file="1687-1812-2011-17-i3.gif"/></inline-formula> 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.</p> <p><b>2000 MSC: </b>26B25, 40A05</p>