$A$-statistical convergence of Mittag-Leffler operators

Abstract

In this paper we introduce the Mittag-Leffler operators, which includes the modified Szász-Mirakjan operators. We obtain the transformation properties and compute the rate of convergence by using modulus of continuity. Furthermore we give the A-statistical approximation theorem for these operators.

q-analogue of Mittag-Leffler operators

“…Recently, some authors use A statistical convergence by [2,3,12,13]. Here for a non-negative regular summability matrix A D .a j k /, the definition of A-density of a subset K of N is as…”

“…Note that, forˇD 1 then we get E˛; 1 .´/ D E˛.´/. M.A.Özarslan [12] investigated properties of the following Mittag-Leffler operators…”

“…It is obvious that the operators L .ˇ/ n;q .f I x/ are linear and positive. When q D 1, we have the Mittag-Leffler operators given byÖzarslan [12]. When q D 1 andˇD 1, we get the modified Szász-Mirakjan operators.…”