On simultaneous approximation by summation-integral type beta operator

الملخص EN

In this paper, we introduced modified summation-integral Beta operator ??, ? ? ; ? in the space ??? of r-times differentiable functions.

The definition of these operators is closely connected with considered functional space.

we studied simultaneous approximation for a new sequence of linear positive operator ??,? ? ; ? .

First, we establish the basic pointwise convergence theorem and the proceed to discuss the Voronovsicoskaja type asymptotic formula.

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