Weak sharp solutions associated with a multidimensional variational-type inequality

Well Posedness of New Optimization Problems with Variational Inequality Constraints

“…Recently, the study of well posedness for vector variational inequalities and the associated optimization problems was formulated by Jayswal and Shalini [29]. On the other hand, an important and interesting extension of variational inequality problems is that of multidimensional variational inequality problems and the corresponding multi-time optimization problems (see [30][31][32][33][34][35][36][37][38][39][40]).…”

Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (p,q)-Calculus

“…Mathematical inequalities play important roles in the study of mathematics as well as in other areas of mathematics because of their wide applications in mathematics and physics; see [1][2][3] for more details. One of the most significant functions used to study many interesting inequalities is convex functions, which are defined as follows:…”

“…Inequality (1) was introduced by C. Hermite [4] and investigated by J. Hadamard [5] in 1893. So far, the Hermite-Hadamard inequality and a variety of refinements of Hermite-Hadamard inequalities have been extensively studied by many researchers; see [6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein for more details.…”

“…Recently, Tunç and Göv [42][43][44] studied the concept of (p, q)-calculus over the intervals [a, b] and gave some new definitions of (p, q)-derivatives and (p, q)-integrals. Moreover, they also derived some of its properties and many integral inequalities as in (1), which is called (p, q)-Hermite-Hadamard inequality, and some new results on (p, q)-calculus of several important integral inequalities. Next, Mehmet Kunt et al [45] proved the left side of the (p, q)-Hermite-Hadamard inequality through (p, q)-differentiable convex and quasiconvex functions, and then, they had some new (p, q)-Hermite-Hadamard inequalities.…”

Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications

“…Thereafter, a systematic study of multi-time problems was initiated by the research group of Udrişte [24][25][26][27]. In this way, a multi-time parameter of evolution approach in optimization theory started to be used and this concept has extensively been explored; see [28][29][30]. Apart from optimization, the concept of a multi-time parameter of evolution is also used in space theory.…”