On New Generalized Mitrinović-Adamović-Type Inequalities
In this paper, we establish new generalized Mitrinović-Adamović-type inequalities in a wider range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>,<...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/7/1174 |
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| Summary: | In this paper, we establish new generalized Mitrinović-Adamović-type inequalities in a wider range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>π</mi><mo>)</mo></mrow></semantics></math></inline-formula> by using the monotonicity of certain functions. These inequalities contain sharp and tractable bounds for the function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mfenced separators="" open="(" close=")"><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mi>x</mi></mrow><mi>x</mi></mfrac></mstyle></mfenced><mn>3</mn></msup><mo>.</mo></mrow></semantics></math></inline-formula> All the main results are also true in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mo>−</mo><mi>π</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula> due to the symmetry of the curves involved. |
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| ISSN: | 2227-7390 |