In this paper we introduce the Blackman- and Rogosinski-type approximation processes in an abstract Banach space setting. The historical roots of these processes go back to W. W. Rogosinski in 1926. The given new definitions use a cosine operator functions concept. We prove that in the presented setting the Blackman- and Rogosinski-type operators possess the order of approximation that coincides with results known in trigonometric approximation. Also applications for different types of approximations are given. An application for the Fourier series of symmetric functions with respect to η is emphasized.
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