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Some approximation properties of generalized integral type operators. (English) Zbl 1384.41013
Summary: In this paper we introduce and study the Stancu type generalization of the integral type operators defined in (1.1). First, we obtain the moments of the operators and then prove the Voronovskaja type asymptotic theorem and basic convergence theorem. Next, the rate of convergence and weighted approximation for the above operators are discussed. Then, weighted \(L_{p}\)-approximation and pointwise estimates are studied. Further, we study the \(A\)-statistical convergence of these operators. Lastly, we give better estimations of the above operators using King type approach.

MSC:
41A25 Rate of convergence, degree of approximation
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
40A35 Ideal and statistical convergence
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