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Some new Hadamard-type inequalities via fractional integral operators
Algunas nuevas desigualdades tipo Hadamard a través de operadores integrales fraccionarios
DOI:
https://doi.org/10.15446/recolma.v59n1.122851Palabras clave:
Convex functions, Hadamard's inequality, Hölder's inequality, fractional calculus, special functions (en)Funciones convexas, desigualdad de Hadamard, desigualdad de Hölder, cálculo fraccional, funciones especiales (es)
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The article presents new inequalities of Hadamard-type which are obtained using fractional integral operators belonging to a function whose third-order derivative is convex. The proposed Hadamard-type inequalities have the potential for application in various areas where it is required to estimate the properties of functions with a convex third-order derivative. Examples of functions are given based on a comparative analysis of the estimates of the upper bounds of the Hadamard-type inequalities obtained using the classical and extended H¨older inequalities. Finally, applications to special functions are provided.
El artículo presenta nuevas desigualdades de tipo Hadamard que se obtienen utilizando operadores integrales fraccionarios pertenecientes a una función cuya derivada de tercer orden es convexa. Las desigualdades de tipo Hadamard propuestas tienen potencial de aplicación en diversas áreas donde se requiere estimar las propiedades de funciones con una derivada convexa de tercer orden. Se dan ejemplos de funciones basados en un análisis comparativo de las estimaciones de los límites superiores de las desigualdades de tipo Hadamard obtenidas utilizando las desigualdades Hölder clásica y extendida. Finalmente, se proporcionan aplicaciones a funciones especiales.
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