Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems
In this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/3/229 |
| _version_ | 1797520197253332992 |
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| author | Hari Mohan Srivastava Bidu Bhusan Jena Susanta Kumar Paikray |
| author_facet | Hari Mohan Srivastava Bidu Bhusan Jena Susanta Kumar Paikray |
| author_sort | Hari Mohan Srivastava |
| collection | DOAJ |
| description | In this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful and potentially useful notions. Furthermore, based upon our proposed techniques, we establish the Korovkin-type approximation theorems with algebraic test functions. Finally, we present two illustrative examples under the consideration of positive linear operators in association with the Bernstein polynomials to exhibit the effectiveness of our findings. |
| first_indexed | 2024-03-10T07:53:27Z |
| format | Article |
| id | doaj.art-9a87ad468f324bab97dc27c409f269a1 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T07:53:27Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-9a87ad468f324bab97dc27c409f269a12023-11-22T12:03:19ZengMDPI AGAxioms2075-16802021-09-0110322910.3390/axioms10030229Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation TheoremsHari Mohan Srivastava0Bidu Bhusan Jena1Susanta Kumar Paikray2Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, IndiaDepartment of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, IndiaIn this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful and potentially useful notions. Furthermore, based upon our proposed techniques, we establish the Korovkin-type approximation theorems with algebraic test functions. Finally, we present two illustrative examples under the consideration of positive linear operators in association with the Bernstein polynomials to exhibit the effectiveness of our findings.https://www.mdpi.com/2075-1680/10/3/229riemann integrallebesgue integralstatistical convergencedeferred weighted meanbanach spacepositive linear operators |
| spellingShingle | Hari Mohan Srivastava Bidu Bhusan Jena Susanta Kumar Paikray Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems Axioms riemann integral lebesgue integral statistical convergence deferred weighted mean banach space positive linear operators |
| title | Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems |
| title_full | Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems |
| title_fullStr | Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems |
| title_full_unstemmed | Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems |
| title_short | Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems |
| title_sort | statistical riemann and lebesgue integrable sequence of functions with korovkin type approximation theorems |
| topic | riemann integral lebesgue integral statistical convergence deferred weighted mean banach space positive linear operators |
| url | https://www.mdpi.com/2075-1680/10/3/229 |
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