Table of Contents
Journal of Calculus of Variations
Volume 2013, Article ID 489249, 8 pages
http://dx.doi.org/10.1155/2013/489249
Research Article

Some Approximation Properties of Modified Jain-Beta Operators

1Department of Applied Mathematics & Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchanath Mahadev Road, Surat, Gujarat 395 007, India
2L. 1627 Awadh Puri Colony Beniganj, Phase-III, Opp. I.T.I., Ayodhya Main Road Faizabad, Uttar Pradesh 224 001, India
3Department of Mathematics, St. Xavier College, Ahmedabad, Gujarat 380 009, India

Received 21 May 2013; Revised 24 October 2013; Accepted 3 December 2013

Academic Editor: Jacob Engwerda

Copyright © 2013 Vishnu Narayan Mishra and Prashantkumar Patel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 parameters , , and and discuss Voronovskaja asymptotic formula.