(p, q)‐Generalization of Szász–Mirakyan operators. (19th November 2015)

• Record Type: Journal Article
• Authors: Acar, Tuncer
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 10(2016:Jul. 15)
• Page Start: 2685
• Page End: 2695
• Publication Date: 2015-11-19
• Subjects: (p, q)‐integers -- (p, q)‐Szász–Mirakyan operators -- weighted approximation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3721
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we introduce new modifications of Szász–Mirakyan operators based on ( p, q )‐integers. We first give a recurrence relation for the moments of new operators and present explicit formula for the moments and central moments up to order 4. Some approximation properties of new operators are explored: the uniform convergence over bounded and unbounded intervals is established, direct approximation properties of the operators in terms of the moduli of smoothness is obtained and Voronovskaya theorem is presented. For the particular case p = 1, the previous results for q ‐Sz ász–Mirakyan operators are captured. Copyright © 2015 John Wiley & Sons, Ltd.