DOI: https://doi.org/10.15446/recolma.v50n2.62207

New Hermite-Hadamard and Jensen Type Inequalities for h-Convex Functions on Fractal Sets

Nuevas desigualdades del tipo Hermite-Hadamard y Jensen para funciones h-convexas sobre conjuntos fractales

Miguel Vivas¹, Jorge Hernández², Nelson Merentes³

¹ Escuela Superior politécnica del Litoral (ESPOL), Guayaquil, Ecuador, Universidad Centroccidental Lisandro Alvarado, Barquisimeto, Venezuela mvivas@ucla.edu.ve, mjvivas@espol.edu.ec
² Universidad Centroccidental Lisandro Alvarado, Barquisimeto, Venezuela. jorgehernandez@ucla.edu.ve
³ Universidad Central de Venezuela, Caracas, Venezuela. nmerucv@gmail.com

Abstract

In this paper, some new Jensen and Hermite-Hadamard inequalities for h-convex functions on fractal sets are obtained. Results proved in this paper may stimulate further research in this area.

Keywords: generalized convexity, h-convex functions, Fractal sets, Hermite-Hadamard type inequality, Jensen inequality.

Mathematics Subject Classification: 53C21, 53C42.

Resumen

En este artículo, se obtienen algunas nuevas desigualdades del tipo Jensen y Hermite-Hadamard para funciones h-convexas sobre conjuntos fractales. Los resultados probados en este artículo pueden estimular futuras investigaciones en esta área.

Palabras claves: convexidad generalizada, funciones h-convexas, conjuntos fractales, desigualdad del tipo Hermite Hadamard, Desigualdad del tipo Jensen.

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Recibido: marzo de 2016 Aceptado: septiembre de 2016