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

Authors : Mustafa KARA

Pages : 1136-1168

Doi:10.31801/cfsuasmas.1067635

View : 38 | Download : 7

Publication Date : 2022-12-30

Article Type : Research Paper

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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