Strong Converse Results for Linking Operators and Convex Functions
We consider a family Bn,ρc 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, Bn,ρcf is decreasing with respect to ρ. We give two proofs, using various...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/4049167 |
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| author | Ana-Maria Acu Margareta Heilmann Ioan Rasa |
| author_facet | Ana-Maria Acu Margareta Heilmann Ioan Rasa |
| author_sort | Ana-Maria Acu |
| collection | DOAJ |
| description | We consider a family Bn,ρc 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, Bn,ρcf 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 Bn,ρc applied to convex functions. |
| format | Article |
| id | doaj-art-9766858debb94b23a1bdd999471c8ead |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9766858debb94b23a1bdd999471c8ead2025-02-03T06:46:58ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/40491674049167Strong Converse Results for Linking Operators and Convex FunctionsAna-Maria Acu0Margareta Heilmann1Ioan Rasa2Lucian Blaga University of Sibiu, Department of Mathematics and Informatics, Str. Dr. I. Ratiu, No. 5-7, RO-550012 Sibiu, RomaniaSchool of Mathematics and Natural Sciences, University of Wuppertal, Gaußstraße 20, D-42119 Wuppertal, GermanyTechnical University of Cluj-Napoca, Faculty of Automation and Computer Science, Department of Mathematics, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, RomaniaWe consider a family Bn,ρc 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, Bn,ρcf 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 Bn,ρc applied to convex functions.http://dx.doi.org/10.1155/2020/4049167 |
| spellingShingle | Ana-Maria Acu Margareta Heilmann Ioan Rasa Strong Converse Results for Linking Operators and Convex Functions Journal of Function Spaces |
| title | Strong Converse Results for Linking Operators and Convex Functions |
| title_full | Strong Converse Results for Linking Operators and Convex Functions |
| title_fullStr | Strong Converse Results for Linking Operators and Convex Functions |
| title_full_unstemmed | Strong Converse Results for Linking Operators and Convex Functions |
| title_short | Strong Converse Results for Linking Operators and Convex Functions |
| title_sort | strong converse results for linking operators and convex functions |
| url | http://dx.doi.org/10.1155/2020/4049167 |
| work_keys_str_mv | AT anamariaacu strongconverseresultsforlinkingoperatorsandconvexfunctions AT margaretaheilmann strongconverseresultsforlinkingoperatorsandconvexfunctions AT ioanrasa strongconverseresultsforlinkingoperatorsandconvexfunctions |