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In this paper asymptotic equalities are found for the least upper bounds ofdeviations in the uniform metric of de la Vallee Poussin sums on classes of2\pi-periodic (\psi,\beta)-differentiable functions admitting an analyticcontinuation into the given strip of the complex plane. As a consequence,asymptotic equalities are obtained on classes of convolutions of periodicfunctions generated by the Neumann kernel and the polyharmonic Poisson kernel.

Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric