Strong Converse Results for Linking Operators and Convex Functions. (7th December 2020)

• Record Type: Journal Article
• Authors: Acu, Ana-Maria; Heilmann, Margareta; Rasa, Ioan
• Other Names: Ragusa Maria Alessandra Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-12-07
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/4049167
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We consider a family B n, ρ c of operators which is a link between classical Baskakov operators (for ρ = ∞ ) and their genuine Durrmeyer type modification (for ρ = 1 ). First, we prove that for fixed n, c and a fixed convex function f, B n, ρ c f is decreasing with respect to ρ . We give two proofs, using various probabilistic considerations. Then, we combine this property with some existing direct and strong converse results for classical operators, in order to get such results for the operators B n, ρ c applied to convex functions.