The voronovskaya theorem for q-analogue of szasz-mirakjan operators

Abstract EN

-this present paper, we define ?-Analogue sequence of Szasz-Mirakjan Operators ??,?(?, ?) and introduce some direct results of these operators.

First, we show that this sequence of operators ??,?(?, ?) converges to ?(?) as ? tends to ∞.

Also, we defined the ??ℎ order moment ??,?(?) for ??,?(?, ?) and we then find a recurrence relation for ??,?(?).

Finally ,we find and prove a Voronovskaya –type asymptotic formula of this operator.

Keywords: ? −Szasz-Mirakjan Operators, linear positive operators, ??ℎ order moment and Voronovskaya – type asymptotic formula.