Published in Siberian Advances in Mathematics
We consider the individual ergodic theorem for the action of a semigroup of measurepreserving mappings. We estimate the rate of convergence using estimates for the probability of large deviations for the ergodic averages with an essentially bounded averaging function. We find estimates for the rate of convergence of the ergodic averages in the case...
Published in Mathematical Notes
In the paper, quadratic mappings acting from one finite-dimensional space to another are studied. Sufficient conditions for the stable surjectivity of a quadratic surjective mapping (i.e., for the condition that every quadratic mapping sufficiently close to a given one is also surjective) are obtained. The existence problem for nontrivial zeros of ...
Published in Mathematical Notes
Perturbations of the quadratic form minimization problem under quadratic constraints of the type of equalities are considered. The minimum function ω in this problem which, to each perturbation of the original problem, assigns a sharp lower bound in the perturbed problem is studied. Sufficient conditions for the upper and lower semicontinuity of th...
Published in Aequationes mathematicae
The paper is devoted to the functional inequality (called by us Hlawka’s functional inequality) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(x+y)+f(y+z)+f(x+z)\leq...
Published in Computational Mathematics and Mathematical Physics
For the problem of minimizing a quadratic functional subject to quadratic equality constraints, the topological and differential properties of the minimum function are examined. It is assumed that all the quadratic forms appearing in the statement of the problem are determined by simultaneously diagonalizable matrices. Under this assumption, suffic...
Published in Advances in Difference Equations
In this article, we investigate the Hyers-Ulam stability of the following functional equation f(x+2y)+f(x-2y)=f(x+y)+f(x-y)+3f(2y)-6f(y) on quasi-β-normed spaces. 2000 MR Subject Classification: 45J05; 34k30; 34K20.
Published in Advances in Difference Equations
We deal with a Pexider difference f(2x+y)+f(2x-y)-g(x+y)-g(x-y)-2g(2x)+2g(x) where f and g map be a given abelian group (G, +) into a sequentially complete Hausdorff topological vector space. We also investigate the Hyers-Ulam stability of the following Pexiderized functional equation f(2x+y)+f(2x-y)=g(x+y)+g(x-y)+2g(2x)-2g(x) in topological vector...
Let L1(x) and L2(x) be linearized polynomials over Fqn. We determine conditions when the product L1(x) . L2(x) is a planar mapping on Fqn. For a linearized polynomial L over Fqn, let M(L) ={α∈Fqn : L(x) + α x is bijective on Fqn}. We show that the planarity of the product L1(x) . L2(x) is linked with the set M(L) of a suitable linearized polynomial...
Published in Mathematica Slovaca
A synaptic algebra is both a special Jordan algebra and a spectral order-unit normed space satisfying certain natural conditions suggested by the partially ordered Jordan algebra of bounded Hermitian operators on a Hilbert space. The adjective “synaptic”, borrowed from biology, is meant to suggest that such an algebra coherently “ties together” the...
The maximum-length sequences, also called m-sequences, have received a lot of attention since the late 1960s. In terms of linear-feedback shift register (LFSR) synthesis they are usually generated by certain power polynomials over a finite field and in addition are characterized by a low cross correlation and high nonlinearity. We say that such a s...
