Approximation by modified Bernstein polynomials based on real parameters
Ruchi Singh Rajawat, Karunesh Kumar Singh, Vishnu Narayan Mishra
Abstract
In this paper, we introduce a modified Bernstein-type operators based on two real parameters and study its various approximation properties. We derive some direct results e.g. Voronovkaja type asymptotic theorem, an estimate of error in ordinary as well as in Ditzian Totik modulus of smoothness and an error estimate for functions belonging to the Lipschitz type space. Further, we examine the rate of approximation for a Kirov and Popova type generalization of these operators.
Topics & Concepts
Bernstein polynomialMathematicsType (biology)GeneralizationModulus of continuityEquioscillation theoremLipschitz continuitySmoothnessApplied mathematicsSpace (punctuation)Approximation errorMathematical analysisPure mathematicsClassical orthogonal polynomialsOrthogonal polynomialsComputer scienceGegenbauer polynomialsBiologyEcologyOperating systemApproximation Theory and Sequence SpacesMathematical Approximation and IntegrationAdvanced Numerical Analysis Techniques