Related papers: Korovkin-type approximation results through summab…
By extending the classical quantitative approximation results for positive and linear operators in $L^{p}([0, 1]), 1\le p \le +\infty$ of Berens and DeVore in 1978 and of Swetits and Wood in 1983 to the more general case of sublinear,…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations
We give a new proof of the compactness of minimizing sequences of the Sobolev inequalities in the critical case. Our approach relies on a simplified version of the concentration-compactness principle, which does not require any refinement…
Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of…
While Kolmogorov's probability axioms are widely recognized, it is less well known that in an often-overlooked 1930 note, Kolmogorov proposed an axiomatic framework for a unifying concept of the mean -- referred to as regular means. This…
The classical Korovkin theorem traditionally relies on the positivity of the underlying sequence of operators. However, in 1968, D. E. Wulbert established the first non-positive version. In this article, we generalize Wulbert's result to…
This paper is a modified chapter of the author's Ph.D. thesis. We introduce the notions of sequentially approximated types and sequentially approximated Keisler measures. As the names imply, these are types which can be approximated by a…
This paper offers a solution method that allows one to find exact values for a large class of convergent series of rational terms. Sums of this form arise often in problems dealing with Quantum Field Theory.
In this paper, we study a strong inverse approximation theorem and saturation order for the family of Kantorovich exponential sampling operators. The class of log-uniformly continuous and bounded functions, and class of log-H\"{o}lderian…
We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Convex Geometry. In this paper we prove a (sharp)…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
We prove a Tauberian theorem for the Voronoi summation method of divergent series with an estimate of the remainder term. The results on the Voronoi summability are then applied to analyze the mean values of multiplicative functions on…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
The main goal of this paper is to prove a Hermite-Hadamard type inequality for certain Schur convex functions using, as one of the main tools in the proof, a Korovkin-type approximation theorem.
Computational materials design often profits from the fact that some complicated contributions are not calculated for the real material, but replaced by results of models. We turn this approximation into a very general and in principle…
It is well known that Mosco (type) convergence is a tool in order to verify weak convergence of finite dimensional distributions of sequences of stochastic processes. In the present paper we are concerned with the concept of Mosco type…