Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities

By M. Sarıkaya, Erhan Set, H. Yaldiz, N. Basak. Mathematical and computer modelling, 2013

870 citations recorded by the source corpus.

Abstract In the present note, first we have established Hermite–Hadamard’s inequalities for fractional integrals. Second, an integral identity and some Hermite–Hadamard type integral inequalities for the fractional integrals are obtained and these results have some relationships with [S.S. Dragomir, R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (5) (1998), 91–95)].

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f34808d65c31ddc572dc9afeb2fe5e5136bdac1f

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In Applied Mathematics

Citations in the corpus

Generalizations of Hermite--Hadamard type inequalities for MT-convex functions (2016, background): “[22] established the Hermite-Hadamard’s inequalities for fractional integrals as follows.”
On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function (2016, methodology): “14), we obtain the following result proved in [23].”
On the Hermite–Hadamard-type inequalities for co-ordinated convex function via fractional integrals (2014, methodology): “[13] presented the following important integral identity including the first-order derivative of f to establish many interesting Hermite–Hadamard-type inequalities for convex functions via Riemann–Liouville fractional integrals of the order α > 0.”
Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals (2016, background): “Due to the wide application of fractional integrals, some authors extended to study fractional HermiteHadamard, Grüss, or Ostrowski type inequalities for functions of different classes, see [2, 11, 13, 14, 15, 16, 23, 26] where further references are listed.”
Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for generalized fractional integrals ☆ (2016, methodology): “Main Results First we generalize Sarikaya’s results [37] of the Hermite-Hadamard’s inequalities for the Katugampola fractional integrals.”
Generalized Convexity and Integral Inequalities (2015, background): “(7) The inequality (7) is the extension of classical Hermite-Hadamard inequality for relative convex functions.”
Hermite‐Hadamard inequalities for Riemann‐Liouville fractional integrals of a convex function with respect to a monotone function (2019, methodology): “Let us now state the definition of generalized Riemann–Liouville fractional integrals: Definition 1.”
GENERALIZATION OF INEQUALITIES ANALOGOUS TO HERMITE-HADAMARD INEQUALITY VIA FRACTIONAL INTEGRALS (2015, neutral): “For results connected with Hermite–Hadamard type inequalities involving fractional integrals one can see [4, 7, 14].”
ON tgs-CONVEX FUNCTION AND THEIR INEQUALITIES (2015, background): “For some recent results connected with fractional integral inequalities see [1]-[6], [22]-[23].”
The Hermite-Hadamard's inequality for some convex functions via fractional integrals and related results (2011, background): “For some recent results connected with fractional integral inequalities see ([18]-[29]) In [28] Sarkaya et.”
New inequalities for fractional integrals and their applications (2016, background): “[11] established the following Hermite–Hadamard-type inequalities for fractional integrals: Theorem D Let f : [a, b] → R be positive with 0 ≤ a < b and f ∈ L1 [a, b] .”
Generalization of different type integral inequalities for s-convex functions via fractional integrals (2013, background): “In recent years, many athors have studied error estimations for Hermite-Hadamard, Ostrowski and Simpson inequalities on the class of s-convex functions in the second sense; for refinements, counterparts, generalization see [2, 3, 5, 9, 10, 12, 13, 16, 17, 18, 19, 20, 21].”
Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions (2016, methodology): “[12] proved the following interesting inequalities of Hermite-Hadamard type involving Riemann-Liouville fractional integrals.”