Abstract
The concept ofη-invex set is explored and the concept ofT-η-invex function is introduced. These concepts are applied to the generalized vector variational inequality problems in ordered topological vector spaces. The study of variational inequality problems is extended toH-spaces and differentiablen-manifolds. The solution of complementarity problem is also studied in the presence of fixed points or Lefschetz number.
Highlights
The concept of η-invex set is explored and the concept of T-η-invex function is introduced. These concepts are applied to the generalized vector variational inequality problems in ordered topological vector spaces
Variational inequality theory has become a rich source of inspiration in pure and applied mathematics
First we extend the concept of η-invex sets and introduce the concept of T-η-invex function and study their applications to the generalized vector variational inequality problems in ordered topological vector spaces
Summary
Variational inequality theory has become a rich source of inspiration in pure and applied mathematics. Classical variational inequality problem has been extended to study a wide class of problems arising in mechanics, physics, optimization and control, nonlinear programming, economics, finance, regional, structural, transportation, elasticity and applied sciences, and so forth. They have been extended and generalized in different directions by using novel and innovative techniques and ideas. First we extend the concept of η-invex sets and introduce the concept of T-η-invex function and study their applications to the generalized vector variational inequality problems in ordered topological vector spaces.
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