Titlebook: Approximation with Positive Linear Operators and Linear Combinations; Vijay Gupta,Gancho Tachev Book 2017 Springer International Publishin

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Direct Estimates for Some New Operators,In this chapter we deal with direct estimates for some integral type operators, established in the recent years.

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,Convergence for Operators Based on Pǎltǎnea Basis,In the year 1987 Chen [36] and Goodman–Sharma [81] introduced the genuine Bernstein polynomials, which preserve linear functions. Some other generalizations of Bernstein polynomials have been introduced and studied in [6, 18, 90, 100, 102, 108, 152] and [171] etc., but they only reproduce constant functions.

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Springer Tracts in Modern Physics 13ry. Apart from the earlier known examples several new sequences of p.l.o. were introduced and their approximation properties have been discussed in the last few decades. There are several books in approximation theory, which deal with the linear and nonlinear operators of different kind. We mention

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Springer Tracts in Modern Physics 13suppose the same definitions for the weight function .(.) and for the domain . of the operators . To establish the inverse results for approximation by .. we need two Bernstein type inequalities and the Berens–Lorentz lemma, which results we formulate as follows:

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