Stancu type generalization of modified Srivastava-Gupta operators

Authors

  • Vishnu Narayan Mishra Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Madhya Pradesh, India L. 1627 Awadh Puri Colony Beniganj, Phase-III, Opposite-Industrial Training Institute (I.T.I.), Faizabad, Uttar Pradesh, India http://orcid.org/0000-0002-2159-7710
  • Alok Kumar Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar, Uttarakhand, India
  • Dipti Tapiawala Department of Mathematics, C U Shah University, Gujarat, India AS and H Department (Mathematics), Sardar Vallabhbhai Patel Institute of Technology, Vasad, Gujarat, India

Keywords:

Srivastava-Gupta operators, rate of convergence, modulus of continuity, weighted approximation, pointwise estimates, A-statistical convergence

Abstract

In this paper, we introduce a Stancu type generalization of modified Srivastava-Gupta operators. We obtain the moments of the operators and then prove the basic convergence theorem. Next, the Voronovskaja type asymptotic formula and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimates using the Lipschitz type maximal function and two parameter Lipschitz-type space. Further, we study the A-statistical convergence of these operators. Lastly, we give better estimations of the above operators using King type approach.

Author Biographies

  • Vishnu Narayan Mishra, Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Madhya Pradesh, India L. 1627 Awadh Puri Colony Beniganj, Phase-III, Opposite-Industrial Training Institute (I.T.I.), Faizabad, Uttar Pradesh, India

    Department of Mathematics, Indira Gandhi National Tribal University, Lalpur,
    Amarkantak, Madhya Pradesh, India

    L. 1627 Awadh Puri Colony Beniganj, Phase-III, Opposite-Industrial Training Institute
    (I.T.I.), Faizabad, Uttar Pradesh, India

  • Alok Kumar, Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar, Uttarakhand, India
    Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar, Uttarakhand, India
  • Dipti Tapiawala, Department of Mathematics, C U Shah University, Gujarat, India AS and H Department (Mathematics), Sardar Vallabhbhai Patel Institute of Technology, Vasad, Gujarat, India

    Department of Mathematics, C U Shah University, Gujarat, India

    AS and H Department (Mathematics), Sardar Vallabhbhai Patel Institute of Technology,
    Vasad, Gujarat, India

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Published

2017-07-11

Issue

Vol. 10 No. 4: (July 2017)

Section

Mathematical Analysis

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How to Cite

Stancu type generalization of modified Srivastava-Gupta operators. (2017). European Journal of Pure and Applied Mathematics, 10(4), 890-907. https://www.ejpam.com/index.php/ejpam/article/view/3018