Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions

Chen, Feixiang; Wu, Shanhe

doi:10.22436/jnsa.009.02.32

Cited by 62 publications

(26 citation statements)

References 11 publications

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“…In recent years, various generalizations, extensions and variants of such inequalities have been obtained (see [20]- [22]). For other recent results concerning Hermite-Hadamard type inequalities through various classes of convex functions, (see [18]) and the references cited therein, also (see [9]- [17]) and the references cited therein.…”

Section: Theorem 1 Let F : I ⊆ R −→ R Be a Convex Function On An Intmentioning

confidence: 99%

Hermite-Hadamard type fractional integral inequalities for generalized (s,m,\varphi)-preinvex functions

Liko¹,

Kashuri²

2017

ntmsci

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Abstract:In the present paper, by using new identity for fractional integrals some new estimates on generalizations of Hermite-Hadamard type inequalities for the class of generalized (s, m, ϕ)-preinvex functions via Riemann-Liouville fractional integral are established. These results not only extend the results appeared in the literature (see [2]), but also provide new estimates on these types. At the end, some applications to special means are given.Keywords: Hermite-Hadamard inequality, Hölder's inequality, power mean inequality, Riemann-Liouville fractional integral, s-convex in the second sense, m-invex, P-function.

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Section: Theorem 1 Let F : I ⊆ R −→ R Be a Convex Function On An Intmentioning

confidence: 99%

Hermite-Hadamard type fractional integral inequalities for generalized (s,m,\varphi)-preinvex functions

Liko¹,

Kashuri²

2017

ntmsci

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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 other recent results concerning Hermite-Hadamard type inequalities through various classes of convex functions, (see [13]) and the references cited therein, also (see [3], [4], [5], [8], [9], [10], [17], [20]) and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Hermite-Hadamard type fractional integral inequalities for MT$_{(m,\varphi)}$-preinvex functions

Kashuri

Liko

2017

Stud. Univ. Babes-Bolyai Math.

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Abstract. In the present paper, a new class of MT (m,ϕ) -preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT (m,ϕ) -preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for MT (m,ϕ) -preinvex functions that are twice differentiable via Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given. These general inequalities give us some new estimates for Hermite-Hadamard type fractional integral inequalities.Mathematics Subject Classification (2010): 26A51, 26A33, 26D07, 26D10, 26D15.

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Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions

Abstract: In this paper, we establish some new Hermite-Hadamard inequalities for s-convex functions via fractional integrals. Some Hermite-Hadamard type inequalities for products of two convex and s-convex functions via Riemann-Liouville integrals are also established.

Cited by 62 publications

References 11 publications

Hermite-Hadamard type fractional integral inequalities for generalized (s,m,\varphi)-preinvex functions

Hermite-Hadamard type fractional integral inequalities for generalized (s,m,\varphi)-preinvex functions

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

Hermite-Hadamard type fractional integral inequalities for MT$_{(m,\varphi)}$-preinvex functions

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