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(p,q)-Generalization of Szász–Mirakyan operators
Scopus
Toplam 136 atıf DOI
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.
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Approximation by Baskakov-Durrmeyer operators based on (p, q)-integers
Scopus
Havuzumuzda 20 atıf almış
In the present paper, we introduce a new sequence of linear positive operators based on (p, q)-integers. To approximate functions over unbounded intervals, we introduce Baskakov-Durrmeyer type operators using the (p, q)-Gamma function. We investigate rate of convergence of new operators in terms of modulus of continuities and obtain their approximation behavior for the functions belonging to Lipschitz class. At the end, we present a modification of new operators preserving the test function x.
Atıf Yapan Makale Bilgileri
Kurumlar (2)
Aligarh Muslim University
Aligarh, India
Selçuk Üniversitesi
Selçuklu, Turkey