DIRECT ESTIMATIONS OF NEW GENERALIZED BASKAKOV–SZASZ OPERATORS

Vijay Gupta, Neha Malik

Abstract: Several modifications of the discrete operators are available in the literature. In the recent years, certain modifications of the well-known Baskakov and Szasz–Mirakyan operators have been discussed based on certain parameters. We propose mixed summation-integral type operators and estimate the quantitative asymptotic formula and a global direct result for the special case. For general case, we establish moments and some direct convergence results in ordinary approximation, which includes pointwise approximation, asymptotic formula and a direct result in terms of modulus of continuity.

Keywords: Baskakov operators; Szasz-Mirakyan operators; direct results; modulus of continuity

Classification (MSC2000): 41A25; 41A30

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