Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems

✍ Scribed by Yonghong Yao; Yeol Je Cho; Yeong-Cheng Liou

• Book ID: 111488701
• Publisher: SP Versita
• Year: 2011
• Tongue: English
• Weight: 355 KB
• Volume: 9
• Category: Article
• ISSN: 1895-1074
• DOI: 10.2478/s11533-011-0021-3

✦ Synopsis

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.