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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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