Approximation by a new modification of SZÃZ-mirakyan type operators

الملخص EN

I n this paper, we define and consider a modified Szãsz-Mirakyan type operators to approximate a class of functions integrable on the interval Rº =(0, ∞) and study some direct results in simultaneous approximation for this operator which is denoted by Sn,p (ƒ:x).

First, we study the convergence for the operators Sn,p r (ƒ:x) : r =0, 1, 2, … , as n → ∞ and we prove a Voronovskaja-type asymptotic formula for our operators.

Finally, we obtain an error estimate in terms of modulus of continuity of the function being approximated.