Add to ORKGFor O-regularly varying functions a growth relation is introduced and characterized which gives an easy tool in the comparison of the rate of growth of two such functions at the limit point. In particular, methods based on this relation provide necessary and sufficient conditions in establishing chains of inequalities between functions and their geometric, harmonic, and integral means, in both directions. For periodic functions, for example, it is shown how this growth relation can be used in approximation theory in order to establish equivalence theorems between the best approximation and moduli of smoothness from prescribed inequalities of Jackson and Bernstein type. (orig.)SIGLEAvailable from TIB Hannover: RN 2414(459) / FIZ - Fachinform...
Let f be a measurable, real function defined in a neighbourhood of infinity. The function f is said ...
In the paper, we estimate the uniform norm of a function defined on the real line and having zero in...
open access article distributed under the Creative Commons Attribution License, which per-mits unres...
Abstract. We study the growth of functions which are harmonic in any number of variables. The result...
In the present paper we introduce the notion of harmonicity modulus of order p, for integers p #>...
The study deals with the problem of investigation of the behaviour of upper bounds of deviations of ...
The present paper is concerned with the rational approximation of functions holomorphic on a domain ...
The approximation theory contains many statements where the rate of approximation of a function by ...
Using Jackson's and Bernstein's operators we prove that for every topological space $X$ and an arbi...
AbstractWe describe the correspondence between rates of decrease for various moduli of continuity of...
AbstractPerturbations of functional inequalities are studied by using merely growth conditions in te...
Using Jackson's and Bernstein's operators we prove that forevery topological space $X$ and an arbit...
A function, analytical in some finite simply connected region is considered in the paper aiming at t...
This book discusses the Tauberian conditions under which convergence follows from statistical summab...
Some results on approximation of periodic functions are extended in two directions: Improving the de...
Let f be a measurable, real function defined in a neighbourhood of infinity. The function f is said ...
In the paper, we estimate the uniform norm of a function defined on the real line and having zero in...
open access article distributed under the Creative Commons Attribution License, which per-mits unres...
Abstract. We study the growth of functions which are harmonic in any number of variables. The result...
In the present paper we introduce the notion of harmonicity modulus of order p, for integers p #>...
The study deals with the problem of investigation of the behaviour of upper bounds of deviations of ...
The present paper is concerned with the rational approximation of functions holomorphic on a domain ...
The approximation theory contains many statements where the rate of approximation of a function by ...
Using Jackson's and Bernstein's operators we prove that for every topological space $X$ and an arbi...
AbstractWe describe the correspondence between rates of decrease for various moduli of continuity of...
AbstractPerturbations of functional inequalities are studied by using merely growth conditions in te...
Using Jackson's and Bernstein's operators we prove that forevery topological space $X$ and an arbit...
A function, analytical in some finite simply connected region is considered in the paper aiming at t...
This book discusses the Tauberian conditions under which convergence follows from statistical summab...
Some results on approximation of periodic functions are extended in two directions: Improving the de...
Let f be a measurable, real function defined in a neighbourhood of infinity. The function f is said ...
In the paper, we estimate the uniform norm of a function defined on the real line and having zero in...
open access article distributed under the Creative Commons Attribution License, which per-mits unres...