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Rate of approximation by $$q$$-Durrmeyer operators in $$L_p([0,1])$$, $$1\leq p\leq\infty$$. (English) Zbl 1369.41019
Summary: We obtain global rates of approximation by $$q$$-Durrmeyer operators $$D_{n,q}(f;x)$$ for the functions in the class $$L_{p}([0,1])$$, $$1\leq p\leq \infty$$. First, rates of approximation in terms of the norms of $$f$$ and $$f'$$ and in terms of the ordinary modulus of smoothness are obtained. Subsequently, we obtain rates of approximation in terms of the generalized modulus of smoothness $$\omega_{\varphi}(f,\delta)$$.
##### MSC:
 41A25 Rate of convergence, degree of approximation 11N80 Generalized primes and integers
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