The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces

Fixexd point theory and applications

Maryam A Alghamdi¹  Hong-Kun Xu²  Naseer Shahzad³ 

[1] Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, China;Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: viscosity;    implicit midpoint rule;    nonexpansive mapping;    projection;    variational inequality;    hierarchical minimization;    nonlinear evolution equation;    47J25;    47N20;    34G20;    65J15;   

DOI  :  10.1186/s13663-015-0282-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces is established. The strong convergence of this technique is proved under certain assumptions imposed on the sequence of parameters. Moreover, it is shown that the limit solves an additional variational inequality. Applications to variational inequalities, hierarchical minimization problems, and nonlinear evolution equations are included.

【 授权许可】

CC BY