THE LEFT RIEMANN-LIOUVILLE FRACTIONAL HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS

被引：19

作者：

Kunt, Mehmet ^{[1
]}

Karapinar, Dunya ^{[1
]}

Turhan, Sercan ^{[2
]}

Iscan, Imdat ^{[2
]}

机构：

[1] Karadeniz Tech Univ, Dept Math, Fac Sci, TR-61080 Trabzon, Turkey

[2] Giresun Univ, Dept Math, Fac Sci & Arts, TR-28200 Giresun, Turkey

来源：

MATHEMATICA SLOVACA | 2019年 / 69卷 / 04期

关键词：

convex functions; Hermite-Hadamard inequalities; left Riemann-Liouville fractional integral; trapezoid type inequalities; midpoint type inequalities; DIFFERENTIABLE MAPPINGS;

D O I：

10.1515/ms-2017-0261

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, with a new approach, a new fractional Hermite-Hadamard type inequalities for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlier studies. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities.

引用

页码：773 / 784

页数：12

共 9 条

[1] [Anonymous], 2014, BASIC THEORY FRACTIO
[2] [Anonymous], APPL MATH LETT
[3] Hadamard J., 1893, J. Math. Pures Appl., V9, P171
[4] Hermite Ch., 1883, Mathesis, V3, P82
[5] Kilbas AA., 2006, Theory and Applications of Fractional Differential Equations, DOI 10.1016/S0304-0208(06)80001-0
[6] Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula
Kirmaci, US
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2004, 147 (01) : 137 - 146
[7] Inequalities for differentiable mappings with application to special means and quadrature formulae
Pearce, CEM
Pecaric, J
[J]. APPLIED MATHEMATICS LETTERS, 2000, 13 (02) : 51 - 55
[8] Roberts A. W., 1973, Convex Functions
[9] Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities
Sarikaya, Mehmet Zeki
Set, Erhan
Yaldiz, Hatice
Basak, Nagihan
[J]. MATHEMATICAL AND COMPUTER MODELLING, 2013, 57 (9-10) : 2403 - 2407

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