On generalized vector variational-like inequalities

Existence Theorem for Vector Quasi-Variational-like Inequalities

“…Motivated and inspired by recent works [4,5,6,7,9,13,14,16,18,19,21] on vector quasi-variational inequalities and vector variational-like inequalities we establish some existence result of solutions for our problem without monotonicity and without compactness.…”

“…Since then, vector variational inequalities and their generalizations have been used as tools to solve vector optimization problems. For the details on vector variational inequalities and their generalizations, we refer to [2,3,4,5,7,9,11,12,13,14,19,20,21].…”

General set-valued vector variational inequality problems

“…In this pape, inspired by the works [1,4,5,9,11,14,17,18,21,22,23,24,25], we give some existence results for the solutions of the problems (2)-(4) and also discuss the coincidence point results.…”

Generalized Vector Equilibrium-Like Problems without Pseudomonotonicity in Banach Spaces

“…Subsequently, many authors investigated vector variational inequalities in abstract spaces, and extended vector variational inequalities to vector equilibrium problems, which include as special cases various problems, for example, vector complementarity problems, vector optimization problems, abstract economical equilibria, and saddle-point problems (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). …”

“…They considered vector variational-like 2 Journal of Inequalities and Applications inequalities for multifunctions under pseudomonotonicity and hemicontinuity conditions. Recently, Khan and Salahuddin [5] also established a vector version of Minty's lemma and applied it to obtain an existence theorem for a class of vector variationallike inequalities for compact-valued multifunctions under similar pseudomonotonicity condition and similar hemicontinuity condition.…”