Strict Feasibility of Variational Inequalities in Reflexive Banach Spaces

Strict feasibility and solvability for vector equilibrium problems in reflexive Banach spaces

“…Some useful properties and interesting applications have been discussed in [25,[29][30][31]. The following result is exacted from Proposition 2.1 of [31].…”

“…Besides coercivity conditions, strict feasibility plays important roles in the solvability of scalar variational inequalities. It has been shown in [22][23][24][25] that a scalar monotone-type variational inequality has a nonempty and bounded solution set if it is strictly feasible. Recently, the concept of strict feasibility was extended to scalar equilibrium problems and vector variational inequalities.…”

Well-posedness by perturbations of mixed variational inequalities in Banach spaces

“…By using (16) and same arguments as in Theorem 4.1, we can prove that z is a solution of MVIðA; f Þ, a contradiction. Thus, fx n g is bounded.…”

“…Some useful properties and interesting applications have been discussed in [1][2][3]16]. The following result is exacted from Proposition 2.1 of [3].…”

Generalized strict feasibility and solvability for generalized vector equilibrium problem with set-valued map in reflexive Banach spaces

“…Generally, the existence of solution for the classical vector equilibrium problem is established under the strict feasibility condition which was originally used in scalar variational inequality and vector variational inequality [14][15][16][17]. This technique can be extended to the scalar equilibrium problem [18].…”