Let T be an Archimedean (continuous) t-norm and ∈]0, 1 2 [. Fodor and Ovchinnikov have studied a relation between the inequality T (max(x− , 0),min(x+ , 1)) T (x, x) and the convexity of the additive generator of T . Here we clarify this relation and answer open problems from previous studies. © 2004 Elsevier B.V. All rights reserved. MSC: primary 03E72; secondary 20M05; 26E50; 68T37

An optimal control problem for an elliptic variational inequality with a source term is considered. The obstacle is the control, and the goal is to keep the solution of the variational inequality close to the desired pro le while the H norm of the obstacle is not too large. The addition of the source term strongly a ects the needed compactness result for the existence of a minimizer.

The Markov-type inequality ‖p′‖[0,1] ≤ cn log(n + 1)‖p‖[0,1] is proved for all polynomials of degree at most n with coefficients from {−1, 0, 1} with an absolute constant c. Here ‖·‖[0,1] denotes the supremum norm on [0, 1]. The Bernstein-type inequality |p′(y)| ≤ c (1 − y)2 ‖p‖[0,1] , y ∈ [0, 1) , is shown for every polynomial p of the form

In this paper we prove some inequalities for convex function of a higher order. The well known Hermite interpolating polynomial leads us to a converse of Jensen inequality for a regular, signed measure and, as a consequence, a generalization of Hadamard and Petrovi c's inequalities. Also, we obtain a new upper bound for the error function of the Hermite interpolating polynomial je H (x)j in ter...

Here we derive a multivariate fractional representation formula involving ordinary partial derivatives of …rst order. Then we prove a related multivariate fractional Ostrowski type inequality with respect to uniform norm. 2010 AMS Mathematics Subject Classi…cation : 26A33, 26D10, 26D15.

Here we collect some notation and basic lemmas used throughout this note. Throughout, for a random variable X, ‖X‖p denotes (E |X|). It is known that ‖ · ‖p is a norm for any p ≥ 1 (Minkowski’s inequality). It is also known ‖X‖p ≤ ‖X‖q whenever p ≤ q. Henceforth, whenever we discuss ‖ · ‖p, we will assume p ≥ 1. Lemma 1 (Khintchine inequality). For any p ≥ 1, x ∈ R, and (σi) independent Rademac...

In this paper, we suggest and analyze a new iterative method for solving some variational inequality involving an accretive operator in Banach spaces. We prove the strong convergence of the proposed iterative method under certain conditions. As a special of the proposed algorithm, we proved that the algorithm converges strongly to the minimum norm solution of some variational inequality. AMS su...

In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. We deduce a useful concentration inequality for sub-gaussian random vectors. Two examples are given to illustrate these results: a concentration of distances between random vectors and subspaces, and a bound on the norms of products of random and deterministic matric...

It is well known that for multipliers f of the Drury-Arveson space H n, ‖f‖∞ does not dominate the operator norm of Mf . We show that in general ‖f‖∞ does not even dominate the essential norm of Mf . A consequence of this is that there exist multipliers f of H n for which Mf fails to be essentially hyponormal, i.e., if K is any compact, self-adjoint operator, then the inequality M∗ f Mf −MfM f ...

In this paper we present integral conductor inequalities connecting the Lorentz p, q-(quasi)norm of a gradient of a function to a one-dimensional integral of the p, q-capacitance of the conductor between two level surfaces of the same function. These inequalities generalize an inequality obtained by the second author in the case of the Sobolev norm. Such conductor inequalities lead to necessary...