A new iterative algorithm of pseudomonotone mappings for equilibrium problems in Hilbert spaces

Journal of inequalities and applications

Jong Kyu Kim¹ 

关键词: strict pseudocontractions;    pseudomonotone;    Lipschitz-type continuous;    equilibrium problems;    fixed points;   

DOI  :  10.1186/1029-242X-2013-128

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce a new algorithm for finding a common element of the set of fixed points of N strict pseudocontractions and the set of solutions of equilibrium problems with a pseudomonotone and Lipschitz-type continuous bifunction. The scheme is motivated by the idea of extragradient methods and fixed point iteration methods. We show that the iterative sequences generated by this algorithm converge strongly to the above mentioned common element under some suitable conditions on algorithm parameters in a real Hilbert space. And also, we consider the variational inequality problems as an application. MSC:46H09, 47H10, 47J25, 65K10.

【 授权许可】

CC BY