Abstract
The solvability of a class of generalized nonlinear variational inequality problems involving multivalued, strongly monotone and strongly Lipschitz (a special type) operators, which are closely associated with generalized nonlinear complementarily problems, is discussed.
Highlights
Variational inequalities and complementarity problems play important roles in applied mathematics, physics, control theory and optimization, equilibrium theory of transportation and economics, mechanics, and engineering sciences
The solvability of a class of generalized nonlinear variational inequality problems involving multivalued, strongly monotone and strongly Lipschitz operators, which are closely associated with generalized nonlinear complementarity problems, is discussed
These problems, especially variational inequality problems, are studied in convex sets, while complementarity problems are approached in convex cone settings leading to equivalences
Summary
Variational inequalities and complementarity problems play important roles in applied mathematics, physics, control theory and optimization, equilibrium theory of transportation and economics, mechanics, and engineering sciences. The solvability of a class of generalized nonlinear variational inequality problems involving multivalued, strongly monotone and strongly Lipschitz (a special type) operators, which are closely associated with generalized nonlinear complementarity problems, is discussed. [u- v, y- x] > 0 for all y in K, is called the generalized nonlinear variational inequality (GNVI) problem.
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