Hermite–Hadamard type inequalities for harmonically convex functions via fractional integrals

Işcan, İ̇mdat; Wu, Shanhe

doi:10.1016/j.amc.2014.04.020

Cited by 114 publications

(76 citation statements)

References 7 publications

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“…A formal definition for harmonically s-convex functions is stated as follows (see [7,9]): Definition 1.5 ( [7,9]). A function f : I ⊆ R + = (0, +∞) → R is said to be harmonically s-convex function of second kind, where s ∈ (0, 1], if…”

Section: Definition 14 ([6]mentioning

confidence: 99%

Some Hermite-Hadamard type inequalities for harmonically extended s-convex functions

Li¹,

Wu²

2017

J. Nonlinear Sci. Appl.

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Section: Definition 14 ([6]mentioning

confidence: 99%

Some Hermite-Hadamard type inequalities for harmonically extended s-convex functions

Li¹,

Wu²

2017

J. Nonlinear Sci. Appl.

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“…For further information about this topic, the reader may refer to [3,8,9,11,16,17,18,19,20,21,23,24,27,29,30,31] and references cited therein.…”

Section: Corollary 113 ([28])mentioning

confidence: 99%

Properties and integral inequalities of Hadamard- Simpson type for the generalized (s,m) -preinvex functions

Du¹,

Liao²,

Li³

2016

J. Nonlinear Sci. Appl.

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The authors introduce the concepts of m-invex set, generalized (s, m)-preinvex function, and explicitly (s, m)-preinvex function, provide some properties for the newly introduced functions, and establish new Hadamard-Simpson type integral inequalities for a function of which the power of the absolute of the first derivative is generalized (s, m)-preinvex function. By taking different values of the parameters, Hadamardtype and Simpson-type integral inequalities can be deduced. Furthermore, inequalities obtained in special case present a refinement and improvement of previously known results.

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“…For the properties of harmonically-convex functions and harmonically-s-convex function, we refer the reader to [1,5,6,7,8,10,11] and the reference there in.…”

Section: ) and F Is Harmonically Convex And Nondecreasing Function Thmentioning

confidence: 99%

Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral

Işcan

Turhan²,

Maden³

2016

ntmsci

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Hermite–Hadamard type inequalities for harmonically convex functions via fractional integrals

Cited by 114 publications

References 7 publications

Some Hermite-Hadamard type inequalities for harmonically extended s-convex functions

Some Hermite-Hadamard type inequalities for harmonically extended s-convex functions

Properties and integral inequalities of Hadamard- Simpson type for the generalized (s,m) -preinvex functions

Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral

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