Approximation of functions of two variables by certain linear positive operators

Details Approximation of functions of two variables by certain linear positive operators Approximation of functions of two variables by certain linear positive operators

2007-09-21

arxiv.org/abs/0709.3345v1

Mathematics

Classical Analysis and ODEs

13 pages

Scientific paper

We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an $r$th order generalization of these operators and observe its approximation properties. Furthermore, we study the convergence of the linear positive operators in a weighted space of functions of two variables and find the rate of this convergence using weighted modulus of continuity.

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