Hermite-Hadamard-Fejer Type Inequalities for Strongly (s,m)-Convex Functions with Modulus c, in Second Sense

Bracamonte, Mireya; Giménez, José Carlos Martínez; Vivas-Cortez, Miguel

doi:10.18576/amis/100606

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Theorem 2 Let F: [X Y] ⟶ R Be a Positive Function With1

Strongly Reciprocally Convex Functions1

Introduction1

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Cited by 22 publications

(20 citation statements)

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“…Over the years, many authors have studied and introduced several integral inequalities related to these classes of convex functions. For more information and related results, we refer the interested reader to the papers [3,4,10,19,23].…”

mentioning

confidence: 99%

Generalized Ostrowski-type inequalities involving second derivatives via the Katugampola fractional integrals

Kermausuor¹

2019

J. Nonlinear Sci. Appl.

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In this paper, we provide some Ostrowski-type integral inequalities for functions whose second derivatives belongs to the Lebesgue L q spaces using the Katugampola fractional integrals. We also introduced some new inequalities of Ostrowski-type for functions whose second derivatives in absolute value at some powers are strongly (s, m)-convex with modulus µ 0 (in the second sense). Our results are generalizations of some earlier results in the literature.

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confidence: 99%

Generalized Ostrowski-type inequalities involving second derivatives via the Katugampola fractional integrals

Kermausuor¹

2019

J. Nonlinear Sci. Appl.

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“…e Hadamard inequality is one of the most studied inequalities for fractional integral operators. For some recent work, we refer the readers to [3,[8][9][10][11][12][13][14][15][16][17].…”

Section: Theorem 2 Let F: [X Y] ⟶ R Be a Positive Function Withmentioning

confidence: 99%

“…Definition 2 (see [3]). A function f: [0, ∞) ⟶ R is called strongly (s, m)-convex in the second sense with modulus C ≥ 0, if the following inequality holds:…”

Section: Introductionmentioning

confidence: 99%

Inequalities for Riemann–Liouville Fractional Integrals of Strongly $(s, m)$ -Convex Functions

Zhang

Farid

Akbar

2021

Journal of Mathematics

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The results of this paper provide two Hadamard-type inequalities for strongly s , m -convex functions via Riemann–Liouville fractional integrals and error estimations of well-known fractional Hadamard inequalities. Their special cases are given and connected with the results of some published papers.

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“…On the other hand, in [2] we introduced the notion of harmonically strongly convex function as follows: Definition 2.5. Let I be an interval in R\{0} and let c ∈ R + .…”

Section: Strongly Reciprocally Convex Functionsmentioning

confidence: 99%

On some inequalities for strongly reciprocally convex functions

2018

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Hermite-Hadamard-Fejer Type Inequalities for Strongly (s,m)-Convex Functions with Modulus c, in Second Sense

Cited by 22 publications

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Generalized Ostrowski-type inequalities involving second derivatives via the Katugampola fractional integrals

Generalized Ostrowski-type inequalities involving second derivatives via the Katugampola fractional integrals

Inequalities for Riemann–Liouville Fractional Integrals of Strongly $(s, m)$ -Convex Functions

On some inequalities for strongly reciprocally convex functions

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Hermite-Hadamard-Fejer Type Inequalities for Strongly (s,m)-Convex Functions with Modulus c, in Second Sense

Cited by 22 publications

References 0 publications

Generalized Ostrowski-type inequalities involving second derivatives via the Katugampola fractional integrals

Generalized Ostrowski-type inequalities involving second derivatives via the Katugampola fractional integrals

Inequalities for Riemann–Liouville Fractional Integrals of Strongly s , m -Convex Functions

On some inequalities for strongly reciprocally convex functions

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Inequalities for Riemann–Liouville Fractional Integrals of Strongly $(s, m)$ -Convex Functions