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We present new accretion solutions of a polytropic perfect fluid onto an f®-gravity de Sitter-like black hole. We consider two f®-gravity models and obtain finite-period cyclic flows oscillating between the event and cosmological horizons as well as semi-cyclic critical flows executing a two-way motion from and back to the same horizon. Besides the generalizations and new solutions presented in this work, a corrigendum to Eur. Phys. J. C (2016) 76:280 is provided.

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