Levinson’s Functional in Time Scale Settings
We introduce the Levinson functional on time scales using integral inequality of Levinson’s type in the terms of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math><...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/2/141 |
| _version_ | 1797622338058977280 |
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| author | Josipa Barić |
| author_facet | Josipa Barić |
| author_sort | Josipa Barić |
| collection | DOAJ |
| description | We introduce the Levinson functional on time scales using integral inequality of Levinson’s type in the terms of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>-integral for convex (concave) functions on time scale sets and investigate its properties such as superadditivity and monotonicity. The obtained properties are used to derive the bounds of the given Levinson’s functional and those results provide a refinement and the converse of the known Levinson’s inequality on time scales. Further, we define new types of functionals using weighted generalized and power means on time scales, and prove their properties which can be employed in future works to obtain refinements and converses of known integral inequalities on time scales. |
| first_indexed | 2024-03-11T09:09:50Z |
| format | Article |
| id | doaj.art-44d9d6d2ab2841e98c708ff990da62ac |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T09:09:50Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-44d9d6d2ab2841e98c708ff990da62ac2023-11-16T19:05:50ZengMDPI AGAxioms2075-16802023-01-0112214110.3390/axioms12020141Levinson’s Functional in Time Scale SettingsJosipa Barić0Faculty of Electrical Engineering Mechanical Engineering and Naval Architecture, University of Split, 21000 Split, CroatiaWe introduce the Levinson functional on time scales using integral inequality of Levinson’s type in the terms of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>-integral for convex (concave) functions on time scale sets and investigate its properties such as superadditivity and monotonicity. The obtained properties are used to derive the bounds of the given Levinson’s functional and those results provide a refinement and the converse of the known Levinson’s inequality on time scales. Further, we define new types of functionals using weighted generalized and power means on time scales, and prove their properties which can be employed in future works to obtain refinements and converses of known integral inequalities on time scales.https://www.mdpi.com/2075-1680/12/2/141Levinson’s inequalityJensen’s functionaltime scale calculus |
| spellingShingle | Josipa Barić Levinson’s Functional in Time Scale Settings Axioms Levinson’s inequality Jensen’s functional time scale calculus |
| title | Levinson’s Functional in Time Scale Settings |
| title_full | Levinson’s Functional in Time Scale Settings |
| title_fullStr | Levinson’s Functional in Time Scale Settings |
| title_full_unstemmed | Levinson’s Functional in Time Scale Settings |
| title_short | Levinson’s Functional in Time Scale Settings |
| title_sort | levinson s functional in time scale settings |
| topic | Levinson’s inequality Jensen’s functional time scale calculus |
| url | https://www.mdpi.com/2075-1680/12/2/141 |
| work_keys_str_mv | AT josipabaric levinsonsfunctionalintimescalesettings |