Iterative methods for split variational inclusion and fixed point problem of nonexpansive semigroup in Hilbert spaces

Journal of inequalities and applications

Dao-Jun Wen¹ 

关键词: split variational inclusion;    nonexpansive semigroup;    fixed point;    averaged mapping;    general iterative method;    47H09;    47H10;    47J22;   

DOI  :  10.1186/s13660-014-0528-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce a general iterative method for a split variational inclusion and nonexpansive semigroups in Hilbert spaces. We also prove that the sequences generated by the proposed algorithm converge strongly to a common element of the set of solutions of a split variational inclusion and the set of common fixed points of one-parameter nonexpansive semigroups, which also solves a class of variational inequalities as an optimality condition for a minimization problem. Moreover, a numerical example is given, to illustrate our methods and results, which may be viewed as a refinement and improvement of the previously known results announced by many other authors.

【 授权许可】

CC BY