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Korovkin type error estimates for positive linear operators involving some special functions. (English) Zbl 1176.41019

Summary: 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 \((0,1)\).

MSC:

41A25 Rate of convergence, degree of approximation
41A30 Approximation by other special function classes
41A36 Approximation by positive operators
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
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