Szász-Beta operators via Hermite Polynomial
Nadeem Rao, Avinash Yadav, M. Mursaleen, B. K. Sinha, Nand Kishor Jha
Abstract
The aim of present article is to introduce the Szász-Beta operators in terms of Hermite Polynomial. We calculate some estimates and then discuss convergence theorems and order of approximation in terms of Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in terms of Peetre’s K-functional, second order modulus of smoothness, Lipschitz type space and rth order Lipschitz type maximal function. Lastly, weighted approximation results and statistical approximation theorems are proved.
Topics & Concepts
MathematicsPointwiseHermite polynomialsLipschitz continuityPointwise convergenceModulus of continuityPolynomialSmoothnessOrder (exchange)Type (biology)BETA (programming language)Applied mathematicsPure mathematicsMathematical analysisApproxBiologyEconomicsComputer scienceFinanceOperating systemEcologyProgramming languageApproximation Theory and Sequence SpacesMathematical Approximation and IntegrationAdvanced Harmonic Analysis Research