Auxiliary problem principle extended to variational inequalities
Journal of Optimization Theory and Applications
Mathematical Programming: Series A and B
Some aspects of variational inequalities
Journal of Computational and Applied Mathematics
Perturbed proximal point algorithms for general quasi-variational-like inclusions
Journal of Computational and Applied Mathematics - Fixed point theory with applications in nonlinear analysis
Existence and algorithm of solutions for generalized mixed implicit quasi-variational inequalities
Applied Mathematics and Computation
Resolvent equations for set-valued mixed variational inequalities
Nonlinear Analysis: Theory, Methods & Applications
Equivalence of variational inclusions with resolvent equations
Nonlinear Analysis: Theory, Methods & Applications
A new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mappings
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Set-valued mixed quasi-variational inequalities and implicit resolvent equations
Mathematical and Computer Modelling: An International Journal
Completely Generalized Multivalued Nonlinear Co-Quasi-Variational-Like Inclusions
Computers & Mathematics with Applications
Variational inclusions with a general H-monotone operator in Banach spaces
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
On the existence of solutions to quasivariational inclusion problems
Journal of Global Optimization
AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
Mathematical and Computer Modelling: An International Journal
Composition duality principles for mixed variational inequalities
Mathematical and Computer Modelling: An International Journal
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In this paper, a new notion of J-proximal mapping for a nonconvex lower semicontinuous subdifferentiable proper functional on Banach space is introduced. The existence and Lipschitz continuity of J-proximal mapping of a lower semicontinuous subdifferentiable proper functional are proved. By applying the concept, we introduce and study a new class of completely generalized quasi-variational inclusions in reflexive Banach spaces. A novel and innovative iterative algorithm for finding the approximate solutions is suggested and analyzed. The convergence criteria of the iterative sequences generated by the new iterative algorithm is also given. These algorithm and existence result generalize many known results under Hilbert space setting in recent literature to reflexive Banach spaces.