Sensitivity analysis for system of parametric generalized quasi-variational inclusions involving R-accretive mappings
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, using proximal-point mappings technique of R-accretive mappings and the property of the fixed point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of the system of parametric generalized quasi-variational inclusions involving R-accretive mappings in real uniformly smooth Banach space. Further under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to parameters. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [3, 23, 24, 32, 33, 34].
Abstract
In this paper, using proximal-point mappings technique of R-accretive mappings and the property of the fixed point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of the system of parametric generalized quasi-variational inclusions involving R-accretive mappings in real uniformly smooth Banach space. Further under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to parameters. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [3, 23, 24, 32, 33, 34].
참고문헌 (37)
- S. Adly, "Perturbed algorithms and sensitivity analysis for a general class of variational inclusions", J. Math. Anal. Appl., 201(2), pp.609~630 (1996)
- R. P. Agarwal, "Sensitivity analysis for strongly nonlinear quasi-variational inclusions", Appl. Math. Lett., 13(6), pp.19~24 (2000)
- R. P. Agarwal, "Sensitivity analysis for a new system of generalized nonlinear mixed quasi-variational inclusions", Appl. Math. Lett., 17(3), pp.345~352 (2004)
- J. P. Aubin, "Differential Inclusions: Set-valued Maps and Viability Theory, Grundlehren der Mathematischen Wissenschaften" (1984)
- C. Baiocchi, "Variational and Quasi-variational Inequalities" (1984), John Wiley & Sons, Inc.
- A. Bensoussan, "Applications of Variational Inequalities" (1984), Gauthiers- Villars
- H. Brezis, "´ Equations et in´equations non lin´eaires dans les espaces vectoriels en dualit´e", Ann. Inst. Fourier (Grenoble), 18, pp.115~175 (1968), fasc.
- C. E. Chidume, "Iterative approximation of a solution of a general variational-like inclusion in Banach spaces", Int. J. Math. Math. Sci., (21), pp.1159~1168 (2004)
- I. Cioreneseu, "Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems" (1990), Kluwer Academic Publishers Group
- J. Crank, "Free and Moving Boundary Problems" (1984), The Clarendon Press
- S. Dafermos, "Sensitivity analysis in variational inequalities", Math. Oper. Res., 13(3), pp.421~434 (1988)
- K. Demling, "Nonlinear Functional Analysis" (1985), Springer-Verlag
- V. F. Demyanov, "Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics, Nonconvex Optimization and its Applications" (1996), Kluwer Academic Publishers
- X.-P. Ding, "ensitivity analysis for generalized nonlinear implicit quasi-variational inclusions", Appl. Math. Lett., 17(2), pp.225~235 (2004)
- X.-P. Ding, "On parametric generalized quasi-variational inequalities", J. Optim. Theory Appl., 100(1), pp.195~205 (1999)
- Y.-P. Fang, "H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces", Appl. Math. Lett., 17(6), pp.647~653 (2004)
- G. Fichera, "Problemi elastostatici con vincoli unilaterali: Il problema di Signorini con ambigue condizioni al contorno", Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez., 7, pp.91~140 (1964)
- F. Giannessi, "Variational inequalities and network equilibrium problems", Proceedings of the conference held in Erice, pp.10~25 (1995), Plenum Press
- R. Glowinski, "Numerical Methods For Nonlinear Variational Problems" (1984), Springer-Verlag
- R. Glowinski, "Numerical Analysis of Variational Inequalities" (1981), North-Holland Publishing Co.
- K. Goebel, "Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings" (1984), Marcel Dekker, Inc.
- K. R. Kazmi, "Iterative approximation of a unique solution of a system of variational-like inclusions in real q-uniformly smooth Banach spaces", Nonlinear Anal., 67(3), pp.917~929 (2007)
- K. R. Kazmi, "Sensitivity analysis for parametric generalized implicit quasi-variational-like inclusions involving P-´-accretive mappings", J. Math. Anal. Appl., 337(2), pp.1198~1210 (2008)
- K. R. Kazmi, "Sensitivity analysis for parametric general set-valued mixed variational-like inequality in uniformly smooth Banach space", Math. Inequal. Appl., 10(2), pp.403~415 (2007)
- T. C. Lim, "On fixed point stability for set-valued contractive mappings with applications to generalized differential equations", J. Math. Anal. Appl., 110(2), pp.436~441 (1985)
- Z. Liu, "Sensitivity analysis for parametric completely generalized nonlinear implicit quasivariational inclusions", J. Math. Anal. Appl., 277(1), pp.142~154 (2003)
- J. J. Moreau, "Proximiteet dualite dans un espace hilbertien", Bull. Soc. Math. France, 93, pp.273~299 (1965)
- R. N. Mukherjee, "Sensitivity analysis of generalized variational inequalities", J. Math. Anal. Appl., 167(2), pp.299~304 (1992)
- S. B. Nadler, "Multi-valued contraction mappings", Pacific J. Math., 30, pp.475~488 (1969)
- M. A. Noor, "Sensitivity analysis for quasi-variational inclusions", J. Math. Anal. Appl., 236(2), pp.290~299 (1999)
- M. A. Noor, "Sensitivity analysis framework for general quasi-variational inclusions", Comput. Math. Appl., 44(8), pp.1175~1181 (2002)
- J. Y. Park, "Parametric generalized mixed variational inequalities", Appl. Math. Lett., 17(1), pp.43~48 (2004)
- J. W. Peng, "Sensitivity analysis for parametric completely generalized strongly nonlinear implicit quasi-variational inclusions", Comput. Math. Appl., 50(5), pp.869~880 (2005)
- J. W. Peng, "A new system of generalized mixed quasi-variational inclusions with (H, ´)-monotone operators", J. Math. Anal. Appl., 327(1), pp.175~187 (2007)
- S. M. Robinson, "Sensitivity analysis of variational inequalities by normal-map techniques, Variational inequalities and network equilibrium problems", pp.257~269 (1995), Plenum
- G. Stampacchia, "Formes bilineaires coercitives sur les ensembles convexes", C. R. Acad. Sci. Paris, 258, pp.4413~4416 (1964)
- N. D. Yen, "H¨older continuity of solutions to a parametric variational inequality", Appl. Math. Optim., 31(3), pp.245~255 (1995)
