Zsolt Páles

Factorization of Minty and Stampacchia variational inequality systems

Abstract In this paper sufficient regularity and coercivity conditions for Minty and Stampacchia type variational inequality systems are offered. The typical results state that if the independent inequalities are solvable, and the functions involved are lower semicontinuous, then the system has also a solution, that is, a factorization principle holds. As an application, a variational inequality system consisting of two partial differential inequalities is considered. This result is analogous to that of Chen [Journal of Mathematical Analysis and Application 231 (1999) 177] obtained for one variational inequality.

Inequalities for Sums of Powers

be valid for all n E N and x , , . . . . x,, > 0 it is necessary ana’ s@cient thut min(a, b) < min(c, d) and max(a, 6) d max(c, d). (5) In [I] Brenner showed independently that (5) is a sufficient condition for (4). He also obtained a number of more general results. There exist other generalizations of Theorem A (see for instance Losonczi [3], Pales [S]) but now we show one way that can also be applied to the inequality (1). Assume that a # b and c #d and then rearrange (4) to obtain l<(,q+ . . . +xy’h-“)(Xf+ . . . +

On Approximately Midconvex Functions

p-h) x (xt’+ ... +xi) I/(< ~ “‘(xf + . . + x;) I/Cd- c). It seems to be natural to consider the following more general inequality

First- and second-order necessary conditions for control problems with constraints

A real-valued function

On approximately convex functions

f

Optimal Control Problems with Set-Valued Control and State Constraints

defined on an open, convex set

On the characterization of quasiarithmetic means with weight function

D

Functional equations involving means and their Gauss composition

of a real normed space is called

Minkowski's inequality for two variable difference means

(\varepsilon,\delta)

On a certain stability of the Hermite–Hadamard inequality

-midconvex if it satisfies