## Abstract and Applied Analysis

### A System of Generalized Variational Inclusions Involving a New Monotone Mapping in Banach Spaces

#### Abstract

We introduce a new monotone mapping in Banach spaces, which is an extension of the ${C}_{n}$-monotone mapping studied by Nazemi (2012), and we generalize the variational inclusion involving the ${C}_{n}$-monotone mapping. Based on the new monotone mapping, we propose a new proximal mapping which combines the proximal mapping studied by Nazemi (2012) with the $\eta$ mapping studied by Lan et al. (2011) and show its Lipschitz continuity. Based on the new proximal mapping, we give an iterative algorithm. Furthermore, we prove the convergence of iterative sequences generated by the algorithm under some appropriate conditions. Our results improve and extend corresponding ones announced by many others.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 654537, 7 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512000

Digital Object Identifier
doi:10.1155/2013/654537

Mathematical Reviews number (MathSciNet)
MR3090285

Zentralblatt MATH identifier
07095210

#### Citation

Guan, Jinlin; Hu, Changsong. A System of Generalized Variational Inclusions Involving a New Monotone Mapping in Banach Spaces. Abstr. Appl. Anal. 2013 (2013), Article ID 654537, 7 pages. doi:10.1155/2013/654537. https://projecteuclid.org/euclid.aaa/1393512000

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