Abstract
The present article deals with the approximation of certain exponential type operators defined by Ismail and May. We estimate the rate of convergence of these operators for functions of bounded variation.
Highlights
Ismail and May [9] studied exponential type operators Ln
The special case p (x) = 2x3/2 leads to the kernel kn (x, t) = e−n√x ne−nt/√x t −1/2 I1
Gupta [5] gave some direct results including an estimate in terms of the second order modulus of continuity and a Voronovskaja-type result for these operators
Summary
Ismail and May [9] studied exponential type operators Ln. Ismail and May [9] studied exponential type operators Ln Many other integral type operators (see, e.g., [1,2,6,7]) including the Phillips operators are not of exponential type. Gupta [5] gave some direct results including an estimate in terms of the second order modulus of continuity and a Voronovskaja-type result for these operators. The recent paper [8] contains a quantitative asymptotic formula in terms of the modulus of continuity with exponential growth, a Korovkin-type result for exponential functions and a Voronovskaja-type asymptotic formula in the simultaneous approximation. The present paper deals with the rate of convergence of the operators Tn for functions of bounded variation
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