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Approximation of functions by Stancu variant of genuine Gupta-Srivastava operators. (English) Zbl 1505.41017

Summary: In the present paper, we introduce the non-negative parametric variant of the genuine Gupta-Srivastava operators, which preserve constant as well as linear functions. We obtain the moments of the operators and then prove the basic convergence theorem. Next, the Voronovskaja-type asymptotic formula and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain pointwise estimates using the Lipschitz-type maximal function and two parameter Lipschitz-type space.

MSC:

41A36 Approximation by positive operators
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
41A81 Weighted approximation
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