On a new system of generalized mixed quasi-variational-like inclusions involving -accretive operators with applications

✍ Scribed by Jian-Wen Peng; Jen-Chih Yao

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 931 KB
• Volume: 234
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.12.001

✦ Synopsis

Existence p-step iterative algorithm Convergence a b s t r a c t

In this paper, we introduce a new and interesting system of generalized mixed quasivariational-like inclusions with (A, η, m)-accretive operators and relaxed cocoercive mappings which contains variational inequalities, variational inclusions, systems of variational inequalities, systems of variational-like inequalities and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (A, η, m)-accretive operators, we prove the existence of solutions and the convergence of a new p-step iterative algorithm for this system of generalized mixed quasi-variationallike inclusions in real q-uniformly smooth Banach spaces. The results in this paper unifies, extends and improves some known results in the literature.