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http://dx.doi.org/10.7858/eamj.2010.26.1.095

VARIATIONAL-LIKE INCLUSION SYSTEMS VIA GENERAL MONOTONE OPERATORS WITH CONVERGENCE ANALYSIS  

Dadashi, Vahid (ISLAMIC AZAD UNIVERSITY-SARI BRANCH)
Roohi, Mehdi (DEPARTMENT OF MATHEMATICS FACULTY OF BASIC SCIENCES UNIVERSITY)
Publication Information
East Asian mathematical journal / v.26, no.1, 2010 , pp. 95-103 More about this Journal
Abstract
In this paper using Lipschitz continuity of the resolvent operator associated with general H-maximal m-relaxed $\eta$-monotone operators, existence and uniqueness of the solution of a variational inclusion system is proved. Also, an iterative algorithm and its convergence analysis is given.
Keywords
Monotone operators; resolvent operator; variational inclusion; iterative algorithm;
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1 F.-Q. Xia, and N.-J. Huang, Variational inclusions with a general H-monotone operator in Banach spaces, Comput. Math. Appl. 54 (2007), 24-30.   DOI   ScienceOn
2 R.-P. Agarwal, and R.-U. Verma, General system of $(A,\;{\eta})$ -maximal relaxed monotone variational inclusion problems based on generalized hybrid algorithms, Commun. Nonlinear Sci. Numer. Simulat.15 (2010), no. 2, 238-251.   DOI   ScienceOn
3 H.-Y. Lan, and L. Cai, Variational convergence of a new proximal algorithm for nonlinear general A-monotone operator equation systems in Banach spaces, Nonlinear Anal. 71 (2009), no.12, 6194-6201.   DOI   ScienceOn
4 R.-U. Verma, A-monotonicity and its role in nonlinear variational inclusions, J. Optim. Theory Appl. 129 (2006), no. 3, 457-467.   DOI   ScienceOn
5 M. Alimohammady, and M. Roohi, On the general proximal mappings, Accepted by International Journal of Mathematical Sciences(IJMS).
6 M. Alimohammady, and M. Roohi, Implicit variational-like inclusions involving general $(H,\;{\eta})$-monotone operators, J. Nonlinear Sci. Appl. 1 (2008), no. 3, 145-154.
7 R.-U. Verma, Approximation solvability of a class of nonlinear set-valued variational inclusions involving $(A,\;{\eta})$ -monotone mappings, J. Math. Anal. Appl. 337 (2008), 969-975.   DOI   ScienceOn
8 R.-P. Agarwal, and R.-U. Verma, General implicit variational inclusion problems based on A-maximal (m)-relaxed monotonicity (AMRM) frameworks, Appl. Math. Comput. 215 (2009), no. 1, 367-379.   DOI   ScienceOn
9 M. Alimohammady, and M. Roohi, A system of generalized variational inclusions in-volving $G-{\eta}$ -monotone mappings, accepted by Bull. Iran Math. Soc.
10 M. Alimohammady, and M. Roohi, Existence and convergence theorems for implicit variational-like inclusion problem involving general H-maximal m-relaxed $\eta$ -monotone operator, submitted.
11 Y.-J. Cho, and H.-Y. Lan, A new class of generalized nonlinear multi-valued quasi-variational-like inclusions with H-monotone mappings, Math. Inequal. Appl. 10 (2007),no. 2, 389-401.
12 Y.-S. Cui, H.-Y. Lan, and Y.-C. Chen, On implicit fuzzy proximal dynamical systems involving general A-monotone operators in Banach spaces, in Proceedingd of the 5th International Conference on Fuzzy Systems and Knowledge Discovery, vol. 1, pp. 615-620, Jinan, China, October, 2008.
13 X.-P. Ding, and F.-Q. Xia, A new class of completely generalized quasi-variational inclusions in Banach spaces, J. Comput. Appl. Math. 147 (2002), 369-383.   DOI   ScienceOn
14 H.-Y. Lan, L.-C. Cai and Z.-S. Liu, General A-monotone operators and perturbed iterations for nonlinear set-valued relaxed cocoercive operator inclusion problems, Appl. Math. Comput. 215 (2009), no. 4, 1583-1592.   DOI   ScienceOn
15 Y.-P. Fang, and N.-J. Huang, A new class of general variational inclusions involving maximal $\eta$ -monotone mappings, Publ. Math. Debrecen 62 (2003), no. 1-2, 83-98.
16 Y.-P. Fang, and N.-J. Huang, H-monotone operator and resolvent operator technique for variational inclusions, Appl. Math. Comput. 145 (2003), 795-803.   DOI   ScienceOn
17 Y.-P. Fang, and N.-J. Huang, Research Report, Sichuan University, 2003.
18 L.-S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), 114-125.   DOI   ScienceOn
19 R.-U. Verma, A-monotonicity and applications to nonlinear variational inclusion problems, J. Appl. Math. Stoch. Anal. 2004 (2004), no. 2, 193-195.   DOI   ScienceOn
20 R.-U. Verma, General over-relaxed proximal point algorithm involving A-maximal relaxed monotone mappings with applications, Nonlinear Anal. 71 (2009), no. 12, e1461-e1472.   DOI   ScienceOn
21 E. Zeidler, Nonlinear Functional Analysis and its Applications II/B: Monotone Operators, Springer-Verlag, Berlin, 1985.
22 Q.-B. Zhang, Generalized implicit variational-like inclusion problems involving $G-{\eta}$ -monotone mappings, Appl. Math. Lett. 20 (2007), 216-221.   DOI   ScienceOn