Approximation properties of the fractional q-integral of Riemann-Liouville integral type Szasz-Mirakyan-Kantorovich operators

Year 2022, Volume: 71 Issue: 4, 1136 - 1168, 30.12.2022

Mustafa Kara

https://doi.org/10.31801/cfsuasmas.1067635

Abstract

In the present paper, we introduce the fractional q-integral of Riemann-Liouville integral type Szász-Mirakyan-Kantorovich operators. Korovkin-type approximation theorem is given and the order of convergence of these operators are obtained by using Lipschitz-type maximal functions, second order modulus of smoothness and Peetre's K-functional. Weighted approximation properties of these operators in terms of modulus of continuity have been investigated. Then, for these operators, we give a Voronovskaya-type theorem. Moreover, bivariate fractional q- integral Riemann-Liouville fractional integral type Szász-Mirakyan-Kantorovich operators are constructed. The last section is devoted to detailed graphical representation and error estimation results for these operators.

Keywords

Szasz-Mirakyan-Kantorovich operators, q-integral of Riemann-Liouville, Voronovskaya-type

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