Operators Obtained by Using Certain Generating Function for Approximation

This paper is concerned with the sequence of positive linear operators obtained by certain generating functions of polynomials and with investigation of its approximation properties in detail. Initially, the convergence theorem is expressed for the sequence constructed in this article using the universal Korovkin-type theorem and then considering the modulus of continuity and the Lipschitz class, an estimate of the degree of approximation is obtained for this sequence of positive linear operators. Moreover, the generalization involving integral of these operators is defined and then their approximation properties are examined.