Solutions existence for two types of mixed variational relation problems

References

• Balaj M. An intersection theorem with applications in minimax theory and equilibrium problem. J. Math. Anal. Appl. 2007;336:363–371.
   Web of Science ®Google Scholar
• Balaj M, Lin LJ. Fixed points, coincidence points and maximal elements with applications to generalized equilibrium problems and minimax theory. Nonlinear Anal. 2009;70:393–403.
   Google Scholar
• Sach PH, Tuan LA. Existence results for set-valued vector quasiequilibrium problems. J. Optim. Theory Appl. 2007;133:229–240.
   Web of Science ®Google Scholar
• Sach PH, Tuan LA. Generalizations of vector quasivariational inclusion problems with set-valued maps. J. Global Optim. 2009;43:23–45.
   Web of Science ®Google Scholar
• Luc DT. An abstract problem in variational analysis. J. Optim. Theory Appl. 2008;138:65–76.
   Web of Science ®Google Scholar
• Hung NV. Sensitivity analysis for generalized quasi-variational relation problems in locally G-convex spaces. Fixed Point Theory Appl. 2012;158:13 p.
   Google Scholar
• Yang Z, Pu YJ. Existence and stability of solutions for maximal element theorem on Hadamard manifolds with applications. Nonlinear Anal. 2012;75:516–525.
   Web of Science ®Google Scholar
• Luc DT, Sarabi E, Soubeyran A. Existence of solutions in variational relation problems without convexity. J. Math. Anal. Appl. 2010;364:544–555.
   Web of Science ®Google Scholar
• Yang Z, Pu YJ. Generalized Knaster-Kuratowski-Mazurkiewicz theorem without convex hull. J. Optim. Theory Appl. 2012;154:17–29.
   Web of Science ®Google Scholar
• Balaj M, Lin LJ. Generalized variational relation problems with applications. J. Optim. Theory Appl. 2011;148:1–13.
   Web of Science ®Google Scholar
• Khanh PQ, Long VST. Invariant-point theorems and existence of solutions to optimization-related problems. J. Global Optim. 2014;58:545–564.
   Web of Science ®Google Scholar
• Lin LJ. Variational relation problems and equivalent form of generalized Fan--Browder fixed point theorems with applications. J. Global Optim. 2012;53:215–229.
   Web of Science ®Google Scholar
• Hung NV. Existence conditions for symmetric generalized quasi-variational inclusion problems. J. Inequal. Appl. 2013;40:12 p.
   Google Scholar
• Pu YJ, Yang Z. Variational relation problem without the KKM property with applications. J. Math. Anal. Appl. 2012;393:256–264.
   Web of Science ®Google Scholar
• Balaj M, Lin LJ. Existence criteria for the solutions of two types of variational relation problems. J. Optim. Theory Appl. 2013;156:232–246.
   Web of Science ®Google Scholar
• Agarwal RP, Balaj M, O’Regan D. A unifying approach to variational relation problems. J. Optim. Theory Appl. 2012;155:417–429.
   Web of Science ®Google Scholar
• Balaj M. Three types of variational relation problems. Taiwanese J. Math. 2013;17:47–61.
   Web of Science ®Google Scholar
• Lin LJ, Balaj M, Ye YC. Quasi-variational relation problems and generalized Ekeland’s variational principle with applications. Optimization. 2014;63:1353–1365.
   Web of Science ®Google Scholar
• Dhara A, Luc DT. A solution method for linear variational relation problems. J. Global Optim. 2014;59:729–756.
   Web of Science ®Google Scholar
• Latif A, Luc DT. Variational relation problems: existence of solutions and fixed points of contraction mappings. Fixed Point Theory Appl. 2013;315:10 p.
   Google Scholar
• Khanh PQ, Luc DT. Stability of solutions in parametric variational relation problems. Set-Valued Anal. 2008;16:1015–1035.
   Google Scholar
• Hung NV. Continuity of solutions for parametric generalized quasi-variational relation problems. Fixed Point Theory Appl. 2012;102:10 p.
   Google Scholar
• Balaj M, Luc DT. On mixed variational relation problems. Comput. Math. Appl. 2010;60:2712–2722.
   Web of Science ®Google Scholar
• Duong TTT. Mixed generalized quasi-equilibrium problems. J. Global Optim. 2013;56:647–667.
   Web of Science ®Google Scholar
• Lin LJ, Wang SY. Simultaneuous variational relation problems and related applications. Comput. Math. Appl. 2009;58:1711–1721.
   Web of Science ®Google Scholar
• Balaj M, Coroianu L. Matching theorems and simultaneous relation problems. Bull. Korean Math. Soc. 2011;48:939–949.
   Web of Science ®Google Scholar
• Tuan LA, Sach PH, Minh NB. Existence results in a general equilibrium problem. Numer. Funct. Anal. Optim. 2013;34:430–450.
   Web of Science ®Google Scholar
• Tuan LA, Lee GM, Sach PH. Upper semicontinuity in a parametric general variational problem and application. Nonlinear Anal. 2010;72:1500–1513.
   Web of Science ®Google Scholar
• Sach PH, Tuan LA, Lee GM. Sensitivity results for a general class of generalized vector quasi-equilibrium problems with set-valued maps. Nonlinear Anal. 2009;71:571–586.
   Web of Science ®Google Scholar
• Anh LQ, Khanh PQ, Qui NQ. About semicontinuity of set-valued maps and stability of quasivariational inclusions. Set-Valued Var. Anal. 2014;22:533–555.
   Web of Science ®Google Scholar
• Aliprantis CD, Border KC. Infinite dimensional analysis. A hitchhiker’s guide. Berlin: Springer; 2006.
   Google Scholar
• Yannelis NC, Prabhakar ND. Existence of maximal elements and equilibria in linear topological spaces. J. Math. Econom. 1983;12:233–245.
   Web of Science ®Google Scholar
• Yuan GXZ. KKM theory and applications in nonlinear analysis. Vol. 218, Monographs and textbooks in pure and applied mathematics. New York (NY): Marcel Dekker Inc; 1999.
   Google Scholar
• Konnov IV. On quasimonotone variational inequalities. J. Optim. Theory Appl. 1998;99:165–181.
   Web of Science ®Google Scholar
• Daniilidis A, Hadjisavvas N. Characterization of nonsmooth semistrictly quasiconvex and strictly quasiconvex functions. J. Optim. Theory Appl. 1999;102:525–536.
   Web of Science ®Google Scholar
• Hadjisavvas N, Schaible S, Wong NC. Pseudomonotone operators: a survey of the theory and its applications. J. Optim. Theory Appl. 2012;152:1–20.
   Web of Science ®Google Scholar
• Fan K. A minimax inequality and applications. In: Shisha O, editor. Inequalities III. New York (NY): Academic Press; 1972. p. 103–113.
   Google Scholar
• Kien BT, Wong NC, Yao JC. Generalized vector variational inequalities with star-pseudomonotone and discontinuous operators. Nonlinear Anal. 2008;68:2859–2871.
   Web of Science ®Google Scholar
• Lin YC. On generalized vector equilibrium problems. Nonlinear Anal. 2009;70:1040–1048.
   Web of Science ®Google Scholar