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

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Abstract

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.

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Authors and Affiliations

  1. Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Road, Surat, 395 007, (Gujarat), India

    Vishnu Narayan Mishra & Prashantkumar Patel

  2. L. 1627 Awadh Puri Colony Beniganj, Phase -III, Opposite - I.T.I., Ayodhya Main Road, Faizabad, 224 001, (Uttar Pradesh), India

    Vishnu Narayan Mishra

  3. Department of Mathematics, St. Xavier College, Ahmedabad, Gujarat, 380 009, India

    Prashantkumar Patel

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  1. Vishnu Narayan Mishra
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Correspondence to Vishnu Narayan Mishra.

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Mishra, V.N., Patel, P. The Durrmeyer type modification of the q-Baskakov type operators with two parameter α and β . Numer Algor 67, 753–769 (2014). https://doi.org/10.1007/s11075-013-9821-9

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  • DOI: https://doi.org/10.1007/s11075-013-9821-9

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