On generalized nonlinear quasivariational inequalities
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we introduce a new generalized nonlinear quasivariational inequality and establish its equivalence with a fixed point problem by using the resolvent operator technique. Utilizing this equivalence, we suggest two iterative schemes, prove two existence theorems of solutions for the generalized nonlinear quasivariational inequality involving generalized cocoercive mapping and establish some convergence results of the sequences generated by the algorithms. Our results include several previously known results as special cases.
Abstract
In this paper, we introduce a new generalized nonlinear quasivariational inequality and establish its equivalence with a fixed point problem by using the resolvent operator technique. Utilizing this equivalence, we suggest two iterative schemes, prove two existence theorems of solutions for the generalized nonlinear quasivariational inequality involving generalized cocoercive mapping and establish some convergence results of the sequences generated by the algorithms. Our results include several previously known results as special cases.
참고문헌 (15)
- R. Ahmad, "An iterative algorithm for generalized nonlinear varia-tional inclusions", Appl. Math. Lett, 13, pp.23~26 (2000)
- M. R. Bai, "Generalized implicit quasivariational inequalities with relaxed Lipschitz and relaxed monotone mappings", Appl. Math. Lett, 12, pp.69~76 (1999)
- H. Brezis, "Opérateurs Maximaux Monotone et Semigoups de Contractions dans les Espaces de Hilbert", ~ (1973)
- L. S. Liu, "Ishikawa and Mann Iterative process with errors for nonlinear strongly accretive mappings in Banach spaces", J. Math. Anal. Appl, 194, pp.114~125 (1995)
- Z. Liu, "Nonlinear quasivariational inequalities and nonlinear resolvent equations", Int. J. Pure Appl. Math, 10(2), pp.141~161 (2004)
- Z. Liu, "Resolvent equations technique for general variational inclusions", Proc. Japan Acad., Ser. A, 78(10), pp.188~193 (2002)
- Z. Liu, "On the generalized nonlinear quasi- variational inclusions", Acta. Math. Inform. Univ. Ostraviensis, 11, pp.81~90 (2003)
- Z. Liu, "Generalized mixed quasi-variational inclusions and generalized mixed resolvent equations for fuzzy mappings", Appl. Math. Comput, 149, pp.879~891 (2004)
- Z. Liu, "On general variational inclusions with noncompact valued mappings", Adv. Nonlinear Var. Inequal, 5(2), pp.11~25 (2002)
- Z. Liu, "The solvability of a class of quasi-variational inequalities", Adv. Nonlinear Var. Inequal, 6(2), pp.69~78 (2003)
- Z. Liu, "Generalized multivalued nonlinear quasi-variational inclusions", Math. Nachr, 253, pp.45~54 (2003)
- Z. Liu, "Convergence and stability of perturbed three-step iterative algo- rithm for completely generalized nonlinear quasi-variational inequalities", Appl. Math. Comput, 149, pp.245~258 (2004)
- S. H. Shim, "Perturbed iterative algorithms with errors for completely generalized strongly nonlinear implicit quasivariational inclusions", J. Inequal. Appl, 5, pp.381~395 (2000)
- A. H. Siddiqi, "General strongly nonlinear variational inequalities", J. Math. Anal. Appl, 166, pp.386~392 (1992)
- J. C. Yao, "Applications of variational inequalities to nonlinear analysis", Appl. Math. Lett, 4, pp.89~92 (1991)