New Diamond-<i>α</i> Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces
In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula&g...
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MDPI AG
2022-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/7/323 |
| _version_ | 1797433851569504256 |
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| author | Ksenija Smoljak Kalamir |
| author_facet | Ksenija Smoljak Kalamir |
| author_sort | Ksenija Smoljak Kalamir |
| collection | DOAJ |
| description | In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula>-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">T</mi></semantics></math></inline-formula> and differential calculus on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">R</mi></semantics></math></inline-formula>, we obtain already-known Steffensen-type inequalities. |
| first_indexed | 2024-03-09T10:22:48Z |
| format | Article |
| id | doaj.art-0455f9e1cc9b4a3c8d5e7d8a2c673dfa |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T10:22:48Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-0455f9e1cc9b4a3c8d5e7d8a2c673dfa2023-12-01T21:53:23ZengMDPI AGAxioms2075-16802022-07-0111732310.3390/axioms11070323New Diamond-<i>α</i> Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure SpacesKsenija Smoljak Kalamir0Faculty of Textile Technology, University of Zagreb, Prilaz Baruna Filipovića 28a, 10000 Zagreb, CroatiaIn this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula>-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">T</mi></semantics></math></inline-formula> and differential calculus on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">R</mi></semantics></math></inline-formula>, we obtain already-known Steffensen-type inequalities.https://www.mdpi.com/2075-1680/11/7/323time scalesdiamond-α integralmeasure spacesSteffensen-type inequalityconvex function |
| spellingShingle | Ksenija Smoljak Kalamir New Diamond-<i>α</i> Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces Axioms time scales diamond-α integral measure spaces Steffensen-type inequality convex function |
| title | New Diamond-<i>α</i> Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces |
| title_full | New Diamond-<i>α</i> Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces |
| title_fullStr | New Diamond-<i>α</i> Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces |
| title_full_unstemmed | New Diamond-<i>α</i> Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces |
| title_short | New Diamond-<i>α</i> Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces |
| title_sort | new diamond i α i steffensen type inequalities for convex functions over general time scale measure spaces |
| topic | time scales diamond-α integral measure spaces Steffensen-type inequality convex function |
| url | https://www.mdpi.com/2075-1680/11/7/323 |
| work_keys_str_mv | AT ksenijasmoljakkalamir newdiamondiaisteffensentypeinequalitiesforconvexfunctionsovergeneraltimescalemeasurespaces |