New Asymptotic Evaluations for Sequences of Linear Positive Operators on $$C_{2\pi }\left( {{\mathbb {R}}}\right) $$

In the paper we give new asymptotic evaluations for sequences of linear positive operators \(V_{n}:C_{2\pi }\left( {{\mathbb {R}}}\right) \rightarrow C_{2\pi }\left( {{\mathbb {R}}}\right) \). Our method of the proof is entirely different than those known in this area. As applications we complete and extend known asymptotic evaluations in this topic.