A Note on Hermite–Hadamard–Fejer Type Inequalities for Functions Whose <i>n</i>-th Derivatives Are <i>m</i>-Convex or (<i>α</i>,<i>m</i>)-Convex Functions
In this paper, we develop some Hermite–Hadamard–Fejér type inequalities for <i>n</i>-times differentiable functions whose absolute values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><...
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| Médium: | Článek |
| Jazyk: | English |
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MDPI AG
2021-12-01
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| Edice: | Axioms |
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| On-line přístup: | https://www.mdpi.com/2075-1680/11/1/16 |
| Shrnutí: | In this paper, we develop some Hermite–Hadamard–Fejér type inequalities for <i>n</i>-times differentiable functions whose absolute values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi></mrow></semantics></math></inline-formula>-th derivatives are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>-convex function. The results obtained in this paper are extensions and generalizations of the existing ones. As a special case, the generalization of the remainder term of the midpoint and trapezoidal quadrature formulas are obtained. |
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| ISSN: | 2075-1680 |