The solution existence of general variational inclusion problems

DOI10.1016/j.jmaa.2006.06.058zbMath1108.49020OpenAlexW1997130825MaRDI QIDQ864642

Phan Quoc Khanh, Nguyen Xuan Hai

Publication date: 12 February 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.06.058

zbMATH Keywords

equilibrium problemsvariational inclusion problemsquasioptimization\(G\)-quasiconvexity and \(G\)-quasiconvexlikeness with respect to a multifunctionimplicit variational inequalitieslower and upper \(C\)-continuity

Mathematics Subject Classification ID

Variational inequalities (49J40) Optimality conditions for problems in abstract spaces (49K27)

Related Items (48)

Special issue dedicated to the 75th birthday of professor Phan Quoc Khanh ⋮ Hausdorff continuity of approximate solution maps to parametric primal and dual equilibrium problems ⋮ On Hölder continuity of solution maps to parametric vector primal and dual equilibrium problems ⋮ A common fixed point theorem with applications to vector equilibrium problems ⋮ Existence of solutions in variational relation problems without convexity ⋮ Topologically-based characterizations of the existence of solutions of optimization-related problems ⋮ Variational relation problems in a general setting ⋮ Systems of quasi-variational relations with applications ⋮ On the existence of solutions to Pareto quasivariational inclusion problems of type I ⋮ Existence results for general inclusions using generalized KKM theorems with applications to minimax problems ⋮ Generalized vector quasivariational inclusion problems with moving cones ⋮ Well-posedness for generalized quasi-variational inclusion problems and for optimization problems with constraints ⋮ On mixed variational relation problems ⋮ On Hölder continuity of approximate solutions to parametric equilibrium problems ⋮ Well-posedness under relaxed semicontinuity for bilevel equilibrium and optimization problems with equilibrium constraints ⋮ Well-posedness for general parametric quasi-variational inclusion problems ⋮ On Hölder calmness of solution mappings in parametric equilibrium problems ⋮ Semicontinuity of solution sets to parametric quasivariational inclusions with applications to traffic networks. I: Upper semicontinuities ⋮ Various kinds of semicontinuity and the solution sets of parametric multivalued symmetric vector quasiequilibrium problems ⋮ Continuity of approximate solution maps of primal and dual vector equilibrium problems ⋮ On Hölder continuity of approximate solution maps to vector equilibrium problems ⋮ An abstract problem in variational analysis ⋮ Factorization of quasi-variational relations systems ⋮ The studies of systems of variational inclusions problems and variational disclusions problems with applications ⋮ Systems of set-valued quasivariational inclusion problems ⋮ System of vector quasi-variational inclusions with some applications ⋮ Generic stability and essential components of generalized KKM points and applications ⋮ Parametric set-valued vector quasi-equilibrium problems ⋮ Alternative principles and their applications ⋮ Well-posedness for systems of generalized mixed quasivariational inclusion problems and optimization problems with constraints ⋮ Simultaneous variational relation problems and related applications ⋮ Sensitivity in mixed generalized vector quasiequilibrium problems with moving cones ⋮ Collective fixed points, generalized games and systems of generalized quasi-variational inclusion problems in topological spaces ⋮ On Hölder calmness and Hölder well-posedness of vector quasi-equilibrium problems ⋮ Semicontinuity of solution sets to parametric quasivariational inclusions with applications to traffic networks. II. Lower semicontinuities applications ⋮ About semicontinuity of set-valued maps and stability of quasivariational inclusions ⋮ Invariant-point theorems and existence of solutions to optimization-related problems ⋮ Sensitivity analysis for multivalued quasiequilibrium problems in metric spaces: Hölder continuity of solutions ⋮ Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally \(FC\)-uniform spaces ⋮ Sensitivity results for a general class of generalized vector quasi-equilibrium problems with set-valued maps ⋮ Generalized KKM-type theorems in GFC-spaces and applications ⋮ Hölder continuity of the unique solution to quasiequilibrium problems in metric spaces ⋮ Generalizations of vector quasivariational inclusion problems with set-valued maps ⋮ On the existence of solutions to quasivariational inclusion problems ⋮ Some existence theorems in nonlinear analysis for mappings on GFC-spaces and applications ⋮ Some results on systems of quasi-variational inclusion problems and systems of generalized quasi-variational inclusion problems ⋮ On Well-Posedness for Perturbed Quasi-Equilibrium and Quasi-Optimization Problems ⋮ On Hölder continuity of solution maps of parametric primal and dual Ky Fan inequalities

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