Approximation results for q-Szãsz : mirakjan type operators

Abstract EN

In this paper, we introduce and study a new type q-Szasz Mirakjan operators Ln (f, qn ; x) based on the q-integers in the case qn E (0,1), where qn → 1 as n → ∞.

First, we prove that these operators are converging to the function being approximated.

Then, we define the m-th order q-moments and find a recurrence relation for these q-moments.

Finally, we prove Voronovskaja-type asymptotic formulas for the operators Ln (f, qn ; x).