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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 bivariate (p,q)-Baskakov-Kantorovich operators
Scopus
Havuzumuzda 35 atıf almış
The present paper deals with the bivariate (p, q)-Baskakov-Kantorovich operators and their approximation properties. First we construct the operators and obtain some auxiliary results such as calculations of moments and central moments, etc. Our main results consist of uniform convergence of the operators via the Korovkin theorem and rate of convergence in terms of modulus of continuity.
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Kurumlar (2)
Gazi Üniversitesi
Ankara, Turkey
Selçuk Üniversitesi
Selçuklu, Turkey