On Some Generalizations of Reverse Dynamic Hardy Type Inequalities on Time Scales
In the present paper, we prove some new reverse type dynamic inequalities on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">T</mi></semantics></math>&...
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| Format: | Article |
| Language: | English |
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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/2075-1680/11/7/336 |
| _version_ | 1827624705511653376 |
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| author | Ahmed A. El-Deeb Clemente Cesarano |
| author_facet | Ahmed A. El-Deeb Clemente Cesarano |
| author_sort | Ahmed A. El-Deeb |
| collection | DOAJ |
| description | In the present paper, we prove some new reverse type dynamic inequalities on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">T</mi></semantics></math></inline-formula>. Our main inequalities are proved by using the chain rule and Fubini’s theorem 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>. Our results extend some existing results in the literature. As special cases, we obtain some new discrete inequalities, quantum inequalities and integral inequalities. |
| first_indexed | 2024-03-09T12:14:28Z |
| format | Article |
| id | doaj.art-091e90fcbce94093a327196f57446ec9 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T12:14:28Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-091e90fcbce94093a327196f57446ec92023-11-30T22:47:47ZengMDPI AGAxioms2075-16802022-07-0111733610.3390/axioms11070336On Some Generalizations of Reverse Dynamic Hardy Type Inequalities on Time ScalesAhmed A. El-Deeb0Clemente Cesarano1Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, EgyptSection of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, ItalyIn the present paper, we prove some new reverse type dynamic inequalities on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">T</mi></semantics></math></inline-formula>. Our main inequalities are proved by using the chain rule and Fubini’s theorem 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>. Our results extend some existing results in the literature. As special cases, we obtain some new discrete inequalities, quantum inequalities and integral inequalities.https://www.mdpi.com/2075-1680/11/7/336reverse Hardy’s inequalitydynamic inequalitytime scale |
| spellingShingle | Ahmed A. El-Deeb Clemente Cesarano On Some Generalizations of Reverse Dynamic Hardy Type Inequalities on Time Scales Axioms reverse Hardy’s inequality dynamic inequality time scale |
| title | On Some Generalizations of Reverse Dynamic Hardy Type Inequalities on Time Scales |
| title_full | On Some Generalizations of Reverse Dynamic Hardy Type Inequalities on Time Scales |
| title_fullStr | On Some Generalizations of Reverse Dynamic Hardy Type Inequalities on Time Scales |
| title_full_unstemmed | On Some Generalizations of Reverse Dynamic Hardy Type Inequalities on Time Scales |
| title_short | On Some Generalizations of Reverse Dynamic Hardy Type Inequalities on Time Scales |
| title_sort | on some generalizations of reverse dynamic hardy type inequalities on time scales |
| topic | reverse Hardy’s inequality dynamic inequality time scale |
| url | https://www.mdpi.com/2075-1680/11/7/336 |
| work_keys_str_mv | AT ahmedaeldeeb onsomegeneralizationsofreversedynamichardytypeinequalitiesontimescales AT clementecesarano onsomegeneralizationsofreversedynamichardytypeinequalitiesontimescales |