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On q ‐analogue of a parametric generalization of Baskakov operators
Author(s) -
Narain Agrawal Purshottam,
Baxhaku Behar,
Shukla Rahul
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7163
Subject(s) - mathematics , bivariate analysis , modulus of continuity , rate of convergence , generalization , baskakov operator , spectral theorem , smoothness , parametric statistics , pure mathematics , moduli , operator theory , type (biology) , mathematical analysis , fourier integral operator , microlocal analysis , statistics , ecology , channel (broadcasting) , physics , quantum mechanics , electrical engineering , biology , engineering
The purpose of this paper is to define a q ‐analogue of a parametric generalization of Baskakov operators introduced by Aral and Erbay (Math. Commun. 24(1) (2019), 119‐131). We establish some local direct results for these operators by means of the modulus of continuity and the Peetre's K ‐functional. Weighted approximation properties are also established. Next, we construct a bivariate case of the above q ‐operators and determine the rate of convergence in terms of the moduli of continuity. A Voronovskaja‐type theorem is derived too. Further, we study the rate of approximation of Bögel continuous and Bögel differentiable functions by the associated generalized Boolean sum (GBS) operators with the aid of mixed modulus of smoothness. We illustrate the rate of approximation of the q ‐operators, their bivariate, and the GBS cases by means of graphics and tables and show that the GBS operators provide better rate of convergence than the bivariate operators.