Multidimensional Kantorovich modifications of exponential sampling series
Tuncer Acar, Sadettin Kursun, Metin Turgay
Abstract
This paper is devoted to construction of multidimensional Kantorovich modifications of exponential sampling series, which allows to approximate suitable measurable functions by considering their mean values on just one section of the function involved. Approximation behaviour of newly constructed operators is investigated at continuity points for log-uniformly continuous functions. The rate of convergence of the series is presented for the same functions by means of logarithmic modulus of continuity. A Voronovskaja type theorem is also presented by means of Mellin derivatives.
Topics & Concepts
MathematicsSeries (stratigraphy)Modulus of continuityLogarithmExponential functionRate of convergenceExponential typeConvergence (economics)Taylor seriesEntire functionSampling (signal processing)Applied mathematicsFunction (biology)Mathematical analysisType (biology)BiologyChannel (broadcasting)Evolutionary biologyFilter (signal processing)Electrical engineeringEngineeringEcologyPaleontologyEconomic growthComputer scienceComputer visionEconomicsApproximation Theory and Sequence SpacesMathematical Approximation and IntegrationMathematical Analysis and Transform Methods