In this paper, it is proved that fractional Hermite-Hadamard inequality and fractional Hermite-Hadamard-Fejér inequality are just results of Hermite-Hadamard-Fejer inequality. After this, a new fractional Hermite-Hadamard inequality which is not a result of Hermite-Hadamard- Fejer inequality and better than given in [9] by Sarıkaya et al. is obtained. Also, a new equality is proved and some new fractional midpoint type inequalities are given. Our results generalizes the results given in [5] by Kırmacı. [ABSTRACT FROM AUTHOR]
İmdat İşcan, Dünya Karapinar, Mehmet Kunt, Sercan Turhan, and Belirlenecek
Subjects
convex functions, Numerical Analysis, Pure mathematics, Control and Optimization, Algebra and Number Theory, Hermite polynomials, Hermite-Hadamard inequalities, 010102 general mathematics, Mathematics::Classical Analysis and ODEs, Type inequality, 01 natural sciences, 010101 applied mathematics, midpoint type inequalities, Hadamard transform, Discrete Mathematics and Combinatorics, 0101 mathematics, Convex function, Riemann-Liouville fractional integrals, Analysis, Mathematics
Abstract
iscan, imdat/0000-0001-6749-0591; Kunt, Mehmet/0000-0002-8730-5370 WOS: 000458493700023 In this paper, it is proved that fractional Hermite-Hadamard inequality and fractional Hermite-Hadamard-Fejer inequality are just results of Hermite-Hadamard-Fejer inequality. After this, a new fractional Hermite-Hadamard inequality which is not a result of Hermite-Hadamard-Fejer inequality and better than given in [9] by Sarikaya et al. is obtained. Also, a new equality is proved and some new fractional midpoint type inequalities are given. Our results generalizes the results given in [5] by Kirmaci.
Published
2018
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