Global Bounds for the Generalized Jensen Functional with Applications
In this article we give sharp global bounds for the generalized Jensen functional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mi>n</mi></msub><mr...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/a2c0c3c2e0ee4ffeb51ad8fdd8335796 |
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| Sumario: | In this article we give sharp global bounds for the generalized Jensen functional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mi>n</mi></msub><mrow><mo stretchy="false">(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>;</mo><mi mathvariant="bold">p</mi><mo>,</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>. In particular, exact bounds are determined for the generalized power mean in terms from the class of Stolarsky means. As a consequence, we obtain the best possible global converses of quotients and differences of the generalized arithmetic, geometric and harmonic means. |
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