We propose easily implementable algorithms for minimizing the norm with pseudomonotone variational inequality constraints. This bilevel problem arises in the Tikhonov regularization method for pseudomonone variational inequalities. Since the solution set of the lower variational inequality is not given explicitly, the available methods of mathematical programming and variational inequality can ...

ABSTRACT. In contemporary applied and computationalmathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent randommatrices. This quantity is controlled by the norm of the expected square of the randommatrix and the expectation of the maximum squared norm achieved by one of the summands; there is also aweak dependence on the dimension of the rand...

The spectral radius of every d× d matrix A is bounded from below by c ‖A‖ ‖A‖, where c = c(d) > 0 is a constant and ‖·‖ is any operator norm. We prove an inequality that generalizes this elementary fact and involves an arbitrary number of matrices. In the proof we use geometric invariant theory. The generalized spectral radius theorem of Berger and Wang is an immediate consequence of our inequa...

In this paper, we propose a new multidimensional inequality index that satisfies a fundamental set of desired properties. We discuss the case where the social evaluation function of welfare depends simultaneously on unidimensional and multidimensional forms of inequality. We show how this mixed social norm interferes with the most popular axioms conceived specifically for multidimensional indic...

The Bohnenblust–Hille inequality says that the l 2m m+1 -norm of the coefficients of an m-homogeneous polynomial P on C is bounded by ‖P‖∞ times a constant independent of n, where ‖ · ‖∞ denotes the supremum norm on the polydisc D. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be C for some C > 1. Combining this improved version of...

We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of expectation of the supremum of “symmetric exponential” processes compared to the Gaussian ones in the Chevet inequality. This is used to give sharp upper estimate for a quantity Γk,m that controls uniformly the Euclidean operator norm of the sub-matrices ...

A Gagliardo–Nirenberg inequality, with application to duality-based a posteriori error estimation in the L 1 norm Dedicated to Professor Boško S. Jovanovi´c on the occasion of his sixtieth birthday Endre Süli We establish the Gagliardo–Nirenberg-type multiplicative interpolation inequality v L 1 (R n) ≤ Cv 1/2 Lip (R n) v 1/2 BV(R n) ∀v ∈ BV(R n), where C is a positive constant, independent of ...

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

In this article we revisit the inequalities of Kato and Ponce concerning the L norm of the Bessel potential J = (1 − ∆) (or Riesz potential D = (−∆)) of the product of two functions in terms of the product of the L norm of one function and the L norm of the the Bessel potential J (resp. Riesz potential D) of the other function. Here the indices p, q, and r are related as in Hölder’s inequality ...

In 1964, Gähler 1 introduced the concept of 2-norm and 2-inner product spaces as generalization of norm and inner product spaces. A systematic presentation of the results related to the theory of 2-inner product spaces can be found in the book in 2, 3 and in list of references in it. Generalization of 2-inner product space for n ≥ 2 was developed by Misiak 4 in 1989. Gunawan and Mashadi 5 in 20...