Turkish Journal of Mathematics

Abstract: In the present paper, we introduce a new sequence of linear positive operators with the help of generating functions. We obtain some Korovkin type approximation properties for these operators and compute rates of convergence by means of the first and second order modulus of continuities and Peetre´s K-functional. In order to obtain explicit expressions for the first and second moment of our operators, we obtain a functional differential equation including our operators. Furthermore, we deal with a modification of our operators converging to integral of function f on the interval (0,1).

Key Words: Positive linear operators, Korovkin-Bohman theorem, Bernstein power series, generating function, Pochhammer symbol, hypergeometric function, Peetre´s K-functional, first and second order modulus of continuities, functional differential equation