Approximation properties of modified Srivastava-Gupta operators based on certain parameter. (English) Zbl 1431.41010

Summary: In the present article, we give a modified form of generalized Srivastava-Gupta operators based on certain parameter which preserve the constant as well as linear functions. First, we estimate moments of the operators and then prove Voronovskaja type theorem. Next, direct approximation theorem, rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimate using the Lipschitz type maximal function. Finaly, we study the \(A\)-statistical convergence of these operators.


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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