On the Durrmeyer-Type Variant and Generalizations of Lototsky–Bernstein Operators
The starting points of the paper are the classic Lototsky–Bernstein operators. We present an integral Durrmeyer-type extension and investigate some approximation properties of this new class. The evaluation of the convergence speed is performed both with moduli of smoothness and with K-functionals o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/10/1841 |
| _version_ | 1797513113554124800 |
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| author | Ulrich Abel Octavian Agratini |
| author_facet | Ulrich Abel Octavian Agratini |
| author_sort | Ulrich Abel |
| collection | DOAJ |
| description | The starting points of the paper are the classic Lototsky–Bernstein operators. We present an integral Durrmeyer-type extension and investigate some approximation properties of this new class. The evaluation of the convergence speed is performed both with moduli of smoothness and with K-functionals of the Peetre-type. In a distinct section we indicate a generalization of these operators that is useful in approximating vector functions with real values defined on the hypercube <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mi>q</mi></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>. The study involves achieving a parallelism between different classes of linear and positive operators, which will highlight a symmetry between these approximation processes. |
| first_indexed | 2024-03-10T06:10:09Z |
| format | Article |
| id | doaj.art-1c766fed478d454c927b5285861e7cb5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T06:10:09Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-1c766fed478d454c927b5285861e7cb52023-11-22T20:09:54ZengMDPI AGSymmetry2073-89942021-10-011310184110.3390/sym13101841On the Durrmeyer-Type Variant and Generalizations of Lototsky–Bernstein OperatorsUlrich Abel0Octavian Agratini1Fachbereich MND, Technische Hochschule Mittelhessen, 61169 Friedberg, GermanyFaculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, RomaniaThe starting points of the paper are the classic Lototsky–Bernstein operators. We present an integral Durrmeyer-type extension and investigate some approximation properties of this new class. The evaluation of the convergence speed is performed both with moduli of smoothness and with K-functionals of the Peetre-type. In a distinct section we indicate a generalization of these operators that is useful in approximating vector functions with real values defined on the hypercube <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mi>q</mi></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>. The study involves achieving a parallelism between different classes of linear and positive operators, which will highlight a symmetry between these approximation processes.https://www.mdpi.com/2073-8994/13/10/1841Lototsky operatorKorovkin theoremmodulus of smoothnessK-functionalDurrmeyer extension |
| spellingShingle | Ulrich Abel Octavian Agratini On the Durrmeyer-Type Variant and Generalizations of Lototsky–Bernstein Operators Symmetry Lototsky operator Korovkin theorem modulus of smoothness K-functional Durrmeyer extension |
| title | On the Durrmeyer-Type Variant and Generalizations of Lototsky–Bernstein Operators |
| title_full | On the Durrmeyer-Type Variant and Generalizations of Lototsky–Bernstein Operators |
| title_fullStr | On the Durrmeyer-Type Variant and Generalizations of Lototsky–Bernstein Operators |
| title_full_unstemmed | On the Durrmeyer-Type Variant and Generalizations of Lototsky–Bernstein Operators |
| title_short | On the Durrmeyer-Type Variant and Generalizations of Lototsky–Bernstein Operators |
| title_sort | on the durrmeyer type variant and generalizations of lototsky bernstein operators |
| topic | Lototsky operator Korovkin theorem modulus of smoothness K-functional Durrmeyer extension |
| url | https://www.mdpi.com/2073-8994/13/10/1841 |
| work_keys_str_mv | AT ulrichabel onthedurrmeyertypevariantandgeneralizationsoflototskybernsteinoperators AT octavianagratini onthedurrmeyertypevariantandgeneralizationsoflototskybernsteinoperators |