APPROXIMATION PROPERTIES OF THE FRACTIONAL q-INTEGRAL OF RIEMANN-LIOUVILLE INTEGRAL TYPE SZASZ-MIRAKYAN-KANTOROVICH OPERATORS

Abstract

In the present paper, we introduce the fractional q-integral of Riemann-Liouville integral type Szasz-Mirakyan-Kantorovich operators. Ko-rovkin-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 approxima-tion 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 Szasz-Mirakyan-Kantorovich operators are constructed.The last section is devoted to detailed graphical representation and error estimation results for these operators.