×

Sensitivity analysis for nonlinear set-valued variational equations in Banach framework. (English) Zbl 1455.47019

Summary: The main purpose of this paper is to study the sensitivity analysis for nonlinear set-valued variational equations based on \((A, \eta)\)-resolvent operator technique. The obtained results encompass a broad model of results.

MSC:

47J22 Variational and other types of inclusions
47H06 Nonlinear accretive operators, dissipative operators, etc.
47H04 Set-valued operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] B. Di Bella, “An existence theorem for a class of inclusions,” Applied Mathematics Letters, vol. 13, no. 3, pp. 15-19, 2000. · Zbl 0994.47058 · doi:10.1016/S0893-9659(99)00179-2
[2] N.-J. Huang and Y.-P. Fang, “A new class of general variational inclusions involving maximal \eta -monotone mappings,” Publicationes Mathematicae Debrecen, vol. 62, no. 1-2, pp. 83-98, 2003. · Zbl 1017.49011
[3] B. S. Lee and Salahuddin, “Sensitivity analysis for generalized nonlinear quasi-variational inclusions,” Nonlinear Analysis Forum, vol. 8, no. 2, pp. 223-232, 2003. · Zbl 1206.47064
[4] R. U. Verma, “Approximation solvability of a class of nonlinear set-valued variational inclusions involving (A,\eta )-monotone mappings,” Journal of Mathematical Analysis and Applications, vol. 337, no. 2, pp. 969-975, 2008. · Zbl 1140.49008 · doi:10.1016/j.jmaa.2007.01.114
[5] N.-J. Huang, “Nonlinear implicit quasi-variational inclusions involving generalized m-accretive mappings,” Archives of Inequalities and Applications, vol. 2, no. 4, pp. 413-425, 2004. · Zbl 1085.49010
[6] Y.-P. Fang and N.-J. Huang, “H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces,” Applied Mathematics Letters, vol. 17, no. 6, pp. 647-653, 2004. · Zbl 1056.49012 · doi:10.1016/S0893-9659(04)90099-7
[7] H.-Y. Lan, Y. J. Cho, and R. U. Verma, “Nonlinear relaxed cocoercive variational inclusions involving (A,\eta )-accretive mappings in Banach spaces,” Computers & Mathematics with Applications, vol. 51, no. 9-10, pp. 1529-1538, 2006. · Zbl 1207.49011 · doi:10.1016/j.camwa.2005.11.036
[8] M. F. Khan and Salahuddin, “Generalized co-complementarity problems in p-uniformly smooth Banach spaces,” JIPAM: Journal of Inequalities in Pure and Applied Mathematics, vol. 7, no. 2, article 66, 11 pages, 2006. · Zbl 1137.49009
[9] M. F. Khan and Salahuddin, “Generalized multivalued nonlinear co-variational inequalities in Banach spaces,” Functional Differential Equations, vol. 14, no. 2-4, pp. 299-313, 2007. · Zbl 1139.49011
[10] H. G. Li, A. J. Xu, and M. M. Jin, “An Ishikawa-hybrid proximal point algorithm for nonlinear set-valued inclusions problem based on (A,\eta )-accretive framework,” Fixed Point Theory and Applications, vol. 2010, Article ID 501293, 12 pages, 2010. · Zbl 1200.49015 · doi:10.1155/2010/501293
[11] N. D. Yen and G. M. Lee, “Solution sensitivity of a class of variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 215, no. 1, pp. 48-55, 1997. · Zbl 0906.49002 · doi:10.1006/jmaa.1997.5607
[12] S. Dafermos, “Sensitivity analysis in variational inequalities,” Mathematics of Operations Research, vol. 13, no. 3, pp. 421-434, 1988. · Zbl 0674.49007 · doi:10.1287/moor.13.3.421
[13] R. L. Tobin, “Sensitivity analysis for variational inequalities,” Journal of Optimization Theory and Applications, vol. 48, no. 1, pp. 191-209, 1986. · Zbl 0557.49004 · doi:10.1007/BF00938597
[14] R. U. Verma, “Sensitivity analysis for relaxed cocoercive nonlinear quasivariational inclusions,” Journal of Applied Mathematics and Stochastic Analysis, vol. 2006, Article ID 52041, 9 pages, 2006. · Zbl 1110.49011 · doi:10.1155/JAMSA/2006/52041
[15] R. U. Verma, “Sensitivity analysis for generalized strongly monotone variational inclusions based on the (A,\eta )-resolvent operator technique,” Applied Mathematics Letters, vol. 19, no. 12, pp. 1409-1413, 2006. · Zbl 1133.49014 · doi:10.1016/j.aml.2006.02.014
[16] J. Kyparisis, “Sensitivity analysis framework for variational inequalities,” Mathematical Programming, vol. 38, no. 2, pp. 203-213, 1987. · doi:10.1007/BF02604641
[17] A. Moudafi, “Mixed equilibrium problems: sensitivity analysis and algorithmic aspect,” Computers & Mathematics with Applications, vol. 44, no. 8-9, pp. 1099-1108, 2002. · Zbl 1103.49301 · doi:10.1016/S0898-1221(02)00218-3
[18] M. A. Noor, “Some recent advances in variational inequalities. II. Other concepts,” New Zealand Journal of Mathematics, vol. 26, no. 2, pp. 229-255, 1997. · Zbl 0889.49006
[19] S. M. Robinson, “Sensitivity analysis of variational inequalities by normal-map techniques,” in Variational Inequalities and Network and Equilibrium Problems, F. Giannessi and A. Maugeri, Eds., pp. 257-269, Plenum, New York, NY, USA, 1995. · Zbl 0861.49009
[20] S. Husain, M. Firdosh Khan, and Salahuddin, “On parametric generalized multivalued co-variational inequalities in Banach spaces,” South East Asian Journal of Mathematics and Mathematical Sciences, vol. 7, no. 1, pp. 19-33, 2008. · Zbl 1188.49009
[21] H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 16, no. 12, pp. 1127-1138, 1991. · Zbl 0757.46033 · doi:10.1016/0362-546X(91)90200-K
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.