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We study some quantitative estimates of the convergence of the iterates of some Rogosinski type operators to their associated cosine functions. We also consider a general cosine counterpart of the quantitative version of Trotter’s theorem on the approximation of C₀-semigroups.

Mathematics Subject Classification (2010): 41A25, 42A10, 47D09.

Keywords: Convergence of iterates of trigonometric polynomials, Rogosinski operators, representation of cosine functions.