Asymptotic behaviour of Jain operators


The topic of the present paper are certain approximation operators acting on the space of continous functions on \([0,+\infty)\) having polynomial growth. The operators which were defined by Jain in 1972 are based on a probability distribution which is called generalized Poisson distribution. As a main result we derive a complete asymptotic expansion for the sequence of these operators.


Ulrich Abel
Technische Hochschule Mittelhessen, Department MND, Wilhelm-Leuschner-Straße 13, 61169 Friedberg, Germany

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Approximation by positive operators; Rate of convergence ; Degree of approximation; Asymptotic approximations · Asymptotic expansions

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U. Abel, O. Agratini, Asymptotic behaviour of Jain operators, Numer Algor 71 (2016), 553–565.


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