Approximation solution for system of generalized ordered variational inclusions with ⊕ operator in ordered Banach space

• Published in: Journal of inequalities and applications 2017, Vol.2017 (1), p.1-13, Article 81
• Main Authors: Sarfaraz, Mohd, Ahmad, MK, Kılıçman, A
• Format: Article
• Language: English
• Subjects: algorithm; Analysis; Applications of Mathematics; Approximation; Banach space; Convergence; Inclusions; Inequalities; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinearity; Operators; ordered Banach space; Proceedings of the International Conference on Analysis and Applications; resolvent; solution; system
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-017-1351-x

The resolvent operator approach is applied to address a system of generalized ordered variational inclusions with ⊕ operator in real ordered Banach space. With the help of the resolvent operator technique, Li et al. (J. Inequal. Appl. 2013:514, 2013 ; Fixed Point Theory Appl. 2014:122, 2014 ; Fixed Point Theory Appl. 2014:146, 2014 ; Appl. Math. Lett. 25:1384-1388, 2012 ; Fixed Point Theory Appl. 2013:241, 2013 ; Eur. J. Oper. Res. 16(1):1-8, 2011 ; Fixed Point Theory Appl. 2014:79, 2014 ; Nonlinear Anal. Forum 13(2):205-214, 2008 ; Nonlinear Anal. Forum 14: 89-97, 2009 ) derived an iterative algorithm for approximating a solution of the considered system. Here, we prove an existence result for the solution of the system of generalized ordered variational inclusions and deal with a convergence scheme for the algorithms under some appropriate conditions. Some special cases are also discussed.