Open AccessGeneral family of exponential operators
Author(s) -
Km. Lipi,
Naokant Deo
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2012043l
Subject(s) - mathematics , lipschitz continuity , modulus of continuity , shift theorem , rate of convergence , bounded variation , bounded function , bivariate analysis , exponential function , generalization , spectral theorem , convergence (economics) , operator theory , smoothness , approximation error , pure mathematics , discrete mathematics , type (biology) , mathematical analysis , fixed point theorem , ecology , channel (broadcasting) , brouwer fixed point theorem , statistics , danskin's theorem , economic growth , electrical engineering , economics , engineering , biology
In this article, we deal with the approximation properties of Ismail-May operators [16] based on a non-negative real parameter ?. We provide some graphs and error estimation table for a numerical example depicting the convergence of our proposed operators. We further define the B?zier variant of these operators and give a direct approximation theorem using Ditizan-Totik modulus of smoothness and a Voronovoskaya type asymptotic theorem. We also study the error in approximation of functions having derivatives of bounded variation. Lastly, we introduce the bivariate generalization of Ismail May operators and estimate its rate of convergence for functions of Lipschitz class.