On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities
In this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta’s inequality are obtained. Some particular cases are also provided. Among others, the celebrated Kittaneh inequality reads: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/7/1432 |
| _version_ | 1797415387079376896 |
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| author | Mohammad W. Alomari Gabriel Bercu Christophe Chesneau |
| author_facet | Mohammad W. Alomari Gabriel Bercu Christophe Chesneau |
| author_sort | Mohammad W. Alomari |
| collection | DOAJ |
| description | In this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta’s inequality are obtained. Some particular cases are also provided. Among others, the celebrated Kittaneh inequality reads: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>w</mi><mfenced open="(" close=")"><mi>T</mi></mfenced><mo>≤</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced separators="" open="∥" close="∥"><mfenced open="|" close="|"><mi>T</mi></mfenced><mo>+</mo><mfenced separators="" open="|" close="|"><msup><mi>T</mi><mo>*</mo></msup></mfenced></mfenced></mrow></semantics></math></inline-formula>. It is proved that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>w</mi><mfenced open="(" close=")"><mi>T</mi></mfenced><mo>≤</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced separators="" open="∥" close="∥"><mfenced open="|" close="|"><mi>T</mi></mfenced><mo>+</mo><mfenced separators="" open="|" close="|"><msup><mi>T</mi><mo>*</mo></msup></mfenced></mfenced><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><munder><mo movablelimits="false" form="prefix">inf</mo><mrow><mfenced open="∥" close="∥"><mi>x</mi></mfenced><mo>=</mo><mn>1</mn></mrow></munder><msup><mfenced separators="" open="(" close=")"><msup><mfenced separators="" open="⟨" close="⟩"><mrow><mfenced open="|" close="|"><mi>T</mi></mfenced><mi>x</mi><mo>,</mo><mi>x</mi></mrow></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><mo>−</mo><msup><mfenced separators="" open="⟨" close="⟩"><mrow><mfenced separators="" open="|" close="|"><msup><mi>T</mi><mo>*</mo></msup></mfenced><mi>x</mi><mo>,</mo><mi>x</mi></mrow></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></mfenced><mn>2</mn></msup></mrow></semantics></math></inline-formula>, which improves on the Kittaneh inequality for symmetric and non-symmetric Hilbert space operators. Other related improvements to well-known inequalities in literature are also provided. |
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| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T05:46:52Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2a0ae1a9c59e497b9e1cdc4696bdf6e02023-12-03T12:20:02ZengMDPI AGSymmetry2073-89942022-07-01147143210.3390/sym14071432On the Dragomir Extension of Furuta’s Inequality and Numerical Radius InequalitiesMohammad W. Alomari0Gabriel Bercu1Christophe Chesneau2Department of Mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid 21110, JordanDepartment of Mathematics and Computer Sciences, “Dunǎrea de Jos” University of Galati, 111, Domneascǎ Street, 800201 Galati, RomaniaDepartment of Mathematics, LMNO, CNRS-Université de Caen, Campus II, Science 3, 14032 Caen, FranceIn this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta’s inequality are obtained. Some particular cases are also provided. Among others, the celebrated Kittaneh inequality reads: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>w</mi><mfenced open="(" close=")"><mi>T</mi></mfenced><mo>≤</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced separators="" open="∥" close="∥"><mfenced open="|" close="|"><mi>T</mi></mfenced><mo>+</mo><mfenced separators="" open="|" close="|"><msup><mi>T</mi><mo>*</mo></msup></mfenced></mfenced></mrow></semantics></math></inline-formula>. It is proved that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>w</mi><mfenced open="(" close=")"><mi>T</mi></mfenced><mo>≤</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced separators="" open="∥" close="∥"><mfenced open="|" close="|"><mi>T</mi></mfenced><mo>+</mo><mfenced separators="" open="|" close="|"><msup><mi>T</mi><mo>*</mo></msup></mfenced></mfenced><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><munder><mo movablelimits="false" form="prefix">inf</mo><mrow><mfenced open="∥" close="∥"><mi>x</mi></mfenced><mo>=</mo><mn>1</mn></mrow></munder><msup><mfenced separators="" open="(" close=")"><msup><mfenced separators="" open="⟨" close="⟩"><mrow><mfenced open="|" close="|"><mi>T</mi></mfenced><mi>x</mi><mo>,</mo><mi>x</mi></mrow></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><mo>−</mo><msup><mfenced separators="" open="⟨" close="⟩"><mrow><mfenced separators="" open="|" close="|"><msup><mi>T</mi><mo>*</mo></msup></mfenced><mi>x</mi><mo>,</mo><mi>x</mi></mrow></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></mfenced><mn>2</mn></msup></mrow></semantics></math></inline-formula>, which improves on the Kittaneh inequality for symmetric and non-symmetric Hilbert space operators. Other related improvements to well-known inequalities in literature are also provided.https://www.mdpi.com/2073-8994/14/7/1432mixed Schwarz inequalityFuruta inequalitynumerical radius inequalities |
| spellingShingle | Mohammad W. Alomari Gabriel Bercu Christophe Chesneau On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities Symmetry mixed Schwarz inequality Furuta inequality numerical radius inequalities |
| title | On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities |
| title_full | On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities |
| title_fullStr | On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities |
| title_full_unstemmed | On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities |
| title_short | On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities |
| title_sort | on the dragomir extension of furuta s inequality and numerical radius inequalities |
| topic | mixed Schwarz inequality Furuta inequality numerical radius inequalities |
| url | https://www.mdpi.com/2073-8994/14/7/1432 |
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