The Durrmeyer type modification of the q-Baskakov type operators with two parameter α and β

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• 作者：Vishnu Narayan Mishra (1) (2)
  Prashantkumar Patel (1) (3)
  
• 关键词：Durrmeyer type operators ; Weighted approximation ; Rate of convergence ; q ; integral ; Stancu operators ; Point ; wise convergent ; 41A25 ; 41A35
• 刊名：Numerical Algorithms
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：67
• 期：4
• 页码：753-769
• 全文大小：303 KB
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• 作者单位：Vishnu Narayan Mishra (1) (2)
  Prashantkumar Patel (1) (3)
  
  1. Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Road, Surat, 395 007, (Gujarat), India
  2. L. 1627 Awadh Puri Colony Beniganj, Phase -III, Opposite - I.T.I., Ayodhya Main Road, Faizabad, 224 001, (Uttar Pradesh), India
  3. Department of Mathematics, St. Xavier College, Ahmedabad, Gujarat, 380 009, India
  
• ISSN：1572-9265

文摘

In this paper, we are dealing with q analogue of Durrmeyer type modified the Baskakov operators with two parameter α and β, which introduces a new sequence of positive linear q-integral operators. We show that this sequence is an approximation process in the polynomial weighted space of continuous function defined on the interval [0, ?. We study moments, weighted approximation properties, the rate of convergence using a weighted modulus of smoothness, asymptotic formula and better error estimation for these operators.