GENERAL NONLINEAR VARIATIONAL INCLUSIONS WITH H-MONOTONE OPERATOR IN HILBERT SPACES
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In this paper, a new class of general nonlinear variational inclusions involving H-monotone is introduced and studied in Hilbert spaces. By applying the resolvent operator associated with H-monotone,we prove the existence and uniqueness theorems of solution for the general nonlinear variational inclusion, construct an iterative algorithm for computing approximation solution of the general nonlinear variational inclusion and discuss the convergence of the iterative sequence generated by the algorithm. The results presented in this paper improve and extend many known results in recent literatures.
Abstract
In this paper, a new class of general nonlinear variational inclusions involving H-monotone is introduced and studied in Hilbert spaces. By applying the resolvent operator associated with H-monotone,we prove the existence and uniqueness theorems of solution for the general nonlinear variational inclusion, construct an iterative algorithm for computing approximation solution of the general nonlinear variational inclusion and discuss the convergence of the iterative sequence generated by the algorithm. The results presented in this paper improve and extend many known results in recent literatures.
참고문헌 (11)
- S. Adly, "Perturbed algorithms and sensitivity analysis for a general class of variational inclusions", J. Math. Anal. Appl., 201(2), pp.609~630 (1996)
- X. P. Ding, "Perturbed proximal point algorithms for generalized quasivariational inclusions", J. Math. Anal. Appl., 210(1), pp.88~101 (1997)
- Y. P. Fang, "H-monotone operator and resolvent operator technique for variational inclusions", Appl. Math. Comput., 145(2), pp.795~803 (2003)
- N. J. Huang, "On the generalized implicit quasivariational inequalities", J. Math. Anal. Appl., 216(1), pp.197~210 (1997)
- N. J. Huang, "Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi-variational inclusions", Comput. Math. Appl., 35(10), pp.1~7 (1998)
- L. S. Liu, "Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces", J. Math. Anal. Appl., 194(1), pp.114~125 (1995)
- Z. Liu, "General strongly nonlinear quasivariational inequalities with relaxed Lipschitz and relaxed monotone mappings", J. Optim. Theory Appl, 114(3), pp.639~656 (2002)
- Z. Liu, "Resolvent equations technique for general variational inclusions", Proc. Japan Acad. Ser. A Math. Sci., 78(10), pp.188~193 (2002)
- N. Q. Nga, "Set-valued nonlinear variational inequalities for H-monotone mappings in nonreflexive Banach spaces", Nonlinear Anal., 52(2), pp.457~465 (2003)
- L. U. Uko, "Strongly nonlinear generalized equations", J. Math. Anal. Appl., 220(1), pp.65~76 (1998)
- L. C. Zeng, "Iterative algorithm for completely generalized set-valued strongly nonlinear mixed variational-like inequalities", Comput. Math. Appl., 50(5), pp.935~945 (2005)