Some Approximation Properties of Modified Jain-Beta Operators. (26th December 2013)

• Record Type: Journal Article
• Authors: Mishra, Vishnu Narayan; Patel, Prashantkumar
• Other Names: Engwerda Jacob Academic Editor.
• Is Part Of: Journal of calculus of variations. Volume 2013(2013)
• Publication Date: 2013-12-26
• Subjects: Calculus of variations -- Periodicals; Calculus of variations; Electronic journals; Periodicals; 515.64
• DOI: 10.1155/2013/489249
• Languages: English
• ISSNs: 2314-6613

Abstract

Abstract : Generalization of Szász-Mirakyan operators has been considered by Jain, 1972. Using these generalized operators, we introduce new sequences of positive linear operators which are the integral modification of the Jain operators having weight functions of some Beta basis function. Approximation properties, the rate of convergence, weighted approximation theorem, and better approximation are investigated for these new operators. At the end, we generalize Jain-Beta operator with three parametersα, β, andγ and discuss Voronovskaja asymptotic formula.