Iterative algorithms for monotone inclusion problems, fixed point problems and minimization problems

Fixexd point theory and applications

Jong Soo Jung¹ 

[1] Department of Mathematics, Dong-A University, Busan, Korea

关键词: maximal monotone operator;    inverse-strongly monotone operator;    strictly pseudocontractive mapping;    fixed points;    variational inequality;    zeros;    minimum norm problem;   

DOI  :  10.1186/1687-1812-2013-272

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We introduce new implicit and explicit iterative schemes for finding a common element of the set of fixed points of k-strictly pseudocontractive mapping and the set of zeros of the sum of two monotone operators in a Hilbert space. Then we establish strong convergence of the sequences generated by the proposed schemes to a common point of two sets, which is a solution of a certain variational inequality. Further, we find the unique solution of the quadratic minimization problem, where the constraint is the common set of two sets mentioned above. As applications, we consider iterative schemes for the Hartmann-Stampacchia variational inequality problem and the equilibrium problem coupled with fixed point problem. MSC:47H05, 47H09, 47H10, 47J05, 47J07, 47J25, 47J20, 49M05.

【 授权许可】

CC BY