References
- R. Ahmad, A. Khaliq and S.S. Irfan. Completely generalized nonlinear variational-like inclusions with noncompact set-valued mappings. Nonlinear Analysis Forum, 7(2):159–166, 2002.
- R. Ahmad and M. Mursaleen. System of generalized H-resolvent equations and the corresponding system of generalized variational inclusions. Hacettepe Journal of Mathematics and Statistics, 41(1):33–45, 2012.
- R. Ahmad and A.H. Siddiqi. Mixed variational-like inclusions and Jη-proximal operator equations in Banach spaces. Journal of Mathematical Analysis and Applications, 327(1):515–524, 2007. http://dx.doi.org/10.1016/j.jmaa.2006.04.054.
- M. Alimohammady and M.K. Kalleji. Generalized super-relaxed proximal point algorithms involving relative A-maximal relaxed accretive in Banach spaces. Advances in Pure and Applied Mathematics, 5(2):55–63, 2014. http://dx.doi.org/10.1515/apam-2013-0007.
- W.F. Ames. Numerical methods for partial differential equations. 3rd Edition, Academic Press, New York, 1992.
- J.P. Aubin and I. Ekeland. Applied Nonlinear Analysis. John Wiley and Sons, New York, 1984.
- C. Baiocchi and A. Capelo. Variational and quasi-variational inequalities. J. Wiley and Sons, New York, London, 1984.
- A. Bnouhachem and M.A. Noor. Numerical comparison between prediction-correction methods for general variational inequalities. Applied Mathematics and Computation, 186(1):496–505, 2007. http://dx.doi.org/10.1016/j.amc.2006.08.001.
- A. Bnouhachem, M.A. Noor and Th.M. Rassias. Three-steps iterative algorithms for mixed variational inequalities. Applied Mathematics and Computation, 183:436–446, 2006. http://dx.doi.org/10.1016/j.amc.2006.05.086.
- H. Br´ezis. Op´erateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. Math. Studies 5, North-Holland, Amsterdam, 1973.
- H.W. Cao. Sensitivity analysis for a system of generalized nonlinear mixed quasi variational inclusions with H-monotone operators. Journal of Applied Mathematics, 2011(Article ID 921835), 2011. http://dx.doi.org/10.1155/2011/921835.
- X.P. Ding. Generalized quasi-variational-like inclusions with nonconvex functionals. Applied Mathematics and Computation, 122(3):267–282, 2001. http://dx.doi.org/10.1016/S0096-3003(00)00027-8.
- X.P. Ding and Ch.L. Lou. Perturbed proximal point algorithms for general quasivariational-like inclusions. Journal of Computational and Applied Mathematics, 113(12):153–165, 2000. http://dx.doi.org/10.1016/S0377-0427(99)00250-2.
- J. Eckstein and B.P. Bertsekas. On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming, 55(1):293–318, 1992. http://dx.doi.org/10.1007/BF01581204.
- M. Fukushima. The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with applications to a traffic equilibrium problem. Mathematical Programming, 72(1):1–15, 1996. http://dx.doi.org/10.1007/BF02592328.
- F. Giannessi. Theorem of alternative, quadratic programs and complementarity problems, Variational inequalities and complementarity problems. Edited by R.W. Cottle, F. Giannessi and J.L. Lions, Variational Inequalities and Complementarity Problems, J. Wiley and Sons, Chichester, England, 1980.
- F. Giannessi and A. Maugeri. Variational inequalities and network equilibrium problems. Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1358-6.
- R. Glowinski, J.L. Lions and R. Tremolieres. Numerical analysis of variational inequalities. North-Holland, Amsterdam, 1981.
- P. Hartmann and G. Stampacchia. On some non-linear elliptic differential-functional equations. Acta Mathematica, 115(1):271–310, 1966. http://dx.doi.org/10.1007/BF02392210.
- S. Haubruge, V.H. Nguyen and J.J. Strodiot. Convergence analysis and applications of the Glowinski-Le Tallec splitting method for finding a zero of the sum of two maximal monotone operators. Journal of Optimization Theory and Applications, 97(3):645–673, 1998. http://dx.doi.org/10.1023/A:1022646327085.
- N.J. Huang. Generalized nonlinear variational inclusions with noncompact valued mappings. Applied Mathematics Letters, 9(3):25–29, 1996. http://dx.doi.org/10.1016/0893-9659(96)00026-2.
- J.K. Kim, H.Y. Lan and Y.J. Cho. Solution sensitivity of generalized nonlinear parametric (A, η, m)-proximal operator system of equations in Hilbert spaces. Journal of Inequalities and Applications, 2014(362), 2014. http://dx.doi.org/10.1186/1029-242X-2014-362.
- H.Y. Lan. Convergence analysis of new over-relaxed proximal point algorithm frameworks with errors and applications to general A-monotone nonlinear inclusion forms. Applied Mathematics and Computation, 230:154–163, 2014. http://dx.doi.org/10.1016/j.amc.2013.12.028.
- C.H. Lee, Q.H. Ansari and J.C. Yao. A perturbed algorithm for strongly nonlinear variational-like inclusions. Bulletin of the Australian Mathematical Society, 62:417–426, 2000. http://dx.doi.org/10.1017/S0004972700018931.
- P.L. Lions and B. Mercier. Splitting algorithms for the sum of two nonlinear operators. SIAM Journal on Numerical Analysis, 16(6):964–979, 1979. http://dx.doi.org/10.1137/0716071.
- A. Moudafi and M.A. Noor. Sensitivity analysis of variational inclusions by the Wiener-Hopf equation technique. Journal of Applied Mathematics and Stochastic Analysis, 12(3):223–232, 1999. http://dx.doi.org/10.1155/S1048953399000210.
- A. Moudafi and M. Thèra. Finding a zero of the sum of two maximal monotone operators. Journal of Optimization Theory and Applications, 94(2):425–448, 1997. http://dx.doi.org/10.1023/A:1022643914538.
- S.B. Nadler. Multi-valued contraction mappings. Pacific Journal of Mathematics, 30(2):475–488, 1969. http://dx.doi.org/10.2140/pjm.1969.30.475.
- M.A. Noor. Some algorithms for general monotone mixed variational inequalities. Mathematical and Computer Modelling, 29(7):1–9, 1999. http://dx.doi.org/10.1016/S0895-7177(99)00058-8.
- Salahuddin and R. Ahmad. Generalized multi-valued nonlinear quasi-variational-like inclusions. Nonlinear Anal. Forum, 6(2):409–416, 2001.
- A.H. Siddiqi and R. Ahmad. Ishikawa type iterative algorithm for completely generalized nonlinear quasi-variational-like inclusions in Banach spaces. Mathematical and Computer Modelling, 45(56):594–605, 2007. http://dx.doi.org/10.1016/j.mcm.2006.07.008.
- R.U. Verma. On generalized variational inequalities involving relaxed Lipschitz and relaxed monotone operators. Journal of Mathematical Analysis and Applications, 213(1):387–392, 1997. http://dx.doi.org/10.1006/jmaa.1997.5556.
- X.J. Zhou and G. Chen. Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities. Journal of Mathematical Analysis and Applications, 132(1):213–225, 1988. http://dx.doi.org/10.1016/0022-247X(88)90054-6.