6533b825fe1ef96bd12833eb

RESEARCH PRODUCT

Strong Converse Results for Linking Operators and Convex Functions

Margareta HeilmannAna Maria AcuIoan Raşa

subject

Pure mathematicsArticle Subject010102 general mathematicsMathematicsofComputing_GENERALProbabilistic logicType (model theory)Mathematical proof01 natural sciences010104 statistics & probabilityTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESBaskakov operatorConverseQA1-939Order (group theory)0101 mathematicsConvex functionLink (knot theory)AnalysisMathematicsMathematics

description

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.

yearjournalcountryeditionlanguage
2020-12-05Journal of Function Spaces
10.1155/2020/4049167https://doaj.org/article/9766858debb94b23a1bdd999471c8ead