Search results for: George Anastassiou

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article

Local fractional integrals involving generalized strongly m-convex mappings

George Anastassiou, Artion Kashuri, Rozana Liko

Arabian Journal of Mathematics > 2019 > 8 > 2 > 95-107

In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets $${\mathbb {R}}^{\alpha }\, (0<\alpha \le 1)$$ Rα(0<α≤1) of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly m-convex, we obtain some new estimates on generalization of...

article

Left general fractional monotone approximation theory

George Anastassiou

Applicationes Mathematicae > 2016 > 43 > 1 > 117-131

We introduce left general fractional Caputo style derivatives with respect to an absolutely continuous strictly increasing function g. We give various examples of such fractional derivatives for different g. Let f be a p-times continuously differentiable function on [a,b], and let L be a linear left general fractional differential operator such that L(f) is non-negative over a closed subinterval I...

article

Approximation by perturbed neural network operators

George Anastassiou

Applicationes Mathematicae > 2015 > 42 > 1 > 57-81

This article deals with the determination of the rate of convergence to the unit of each of three newly introduced perturbed normalized neural network operators of one hidden layer. These are given through the modulus of continuity of the function involved or its high order derivative that appears in the right-hand side of the associated Jackson type inequalities. The activation function is very general,...

article

Vectorial fractional integral inequalities with convexity

George Anastassiou

Open Physics > 2013 > 11 > 10 > 1194-1211

Here we present vectorial general integral inequalities involving products of multivariate convex and increasing functions applied to vectors of functions. As specific applications we derive a wide range of vectorial fractional inequalities of Hardy type. These involve the left and right: Erdélyi-Kober fractional integrals, mixed Riemann-Liouville fractional multiple integrals. Next we produce multivariate...

article

Vectorial fractional integral inequalities with convexity

George Anastassiou

Open Physics > 2013 > 11 > 10 > 1194-1211

article

General uniform approximation theory by multivariate singular integral operators

George Anastassiou

Annales Polonici Mathematici > 2012 > 103 > 1 > 15-25

We study the uniform approximation properties of general multivariate singular integral operators on $ℝ^{N}$, N ≥ 1. We establish their convergence to the unit operator with rates. The estimates are pointwise and uniform. The established inequalities involve the multivariate higher order modulus of smoothness. We list the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular...

article

On global smoothness preservation in complex approximation

George Anastassiou, Sorin Gal

Annales Polonici Mathematici > 2002 > 79 > 3 > 199-205

By using the properties of convergence and global smoothness preservation of multivariate Weierstrass singular integrals, we establish multivariate complex Carleman type approximation results with rates. Here the approximants fulfill the global smoothness preservation property. Furthermore Mergelyan's theorem for the unit disc is strengthened by proving the global smoothness preservation property.

article

Refined rates of bias convergence for generalized L-Statistics in the i.i.d. case

George Anastassiou, Tomasz Rychlik

Applicationes Mathematicae > 1999 > 26 > 4 > 437-455

Using tools of approximation theory, we evaluate rates of bias convergence for sequences of generalized L-statistics based on i.i.d. samples under mild smoothness conditions on the weight function and simple moment conditions on the score function. Apart from standard methods of weighting, we introduce and analyze L-statistics with possibly random coefficients defined by means of positive linear functionals...

article

Representation formulae for (C₀) m-parameter operator semigroups

Mi Zhou, George Anastassiou

Annales Polonici Mathematici > 1996 > 63 > 3 > 247-272

Some general representation formulae for (C₀) m-parameter operator semigroups with rates of convergence are obtained by the probabilistic approach and multiplier enlargement method. These cover all known representation formulae for (C₀) one- and m-parameter operator semigroups as special cases. When we consider special semigroups we recover well-known convergence theorems for multivariate approximation...

article

On some shift invariant integral operators, univariate case

George Anastassiou, Heinz Gonska

Annales Polonici Mathematici > 1995 > 61 > 3 > 225-243

In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance,...

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Keywords

ERDÉLYI-KOBER FRACTIONAL INTEGRALS (2)
FRACTIONAL INTEGRAL (2)
FRACTIONAL RADIAL DERIVATIVE (2)
HARDY VECTORIAL FRACTIONAL INEQUALITY (2)
POINCARÉ VECTORIAL FRACTIONAL INEQUALITY (2)
RATE OF CONVERGENCE (2)
BANACH SPACE (1)
BERNSTEIN OPERATOR (1)
BERNSTEIN-DURRMEYER OPERATOR (1)
BIAS (1)
CONVERGENCE TO THE UNIT WITH RATES (1)
CONVOLUTION TYPE OPERATORS (1)
GENERALIZED L-STATISTIC (1)
GLOBAL SMOOTHNESS PRESERVATION (1)
INEQUALITIES (1)
INTEGRAL OPERATORS (1)
JACKSON TYPE INEQUALITIES (1)
K-FUNCTIONAL (1)
KANTOROVICH OPERATOR (1)
MODULUS OF CONTINUITY (1)
MODULUS OF SMOOTHNESS (1)
MULTI-PARAMETER OPERATOR SEMIGROUPS (1)
MULTIPLIER ENLARGEMENT METHOD (1)
MULTIVARIATE APPROXIMATION (1)
POSITIVE LINEAR OPERATOR (1)
PROBABILISTIC DISTRIBUTION FUNCTION (1)
RANDOM WEIGHTING (1)
REPRESENTATION FORMULAE (1)
SECOND MODULUS OF CONTINUITY (1)
SHAPE PRESERVING OPERATORS (1)
SHARP INEQUALITIES (1)
SHIFT INVARIANT OPERATORS (1)
SUM OF RANDOM VECTORS (1)
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