On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables

Sitthiwirattham, Thanin; Budak, Hüseyın; Kara, Hasan; Ali, Muhammad Aamir; Reunsumrit, Jiraporn

doi:10.3390/sym13091724

Cited by 3 publications

(2 citation statements)

References 38 publications

(39 reference statements)

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“…In the literature, there are several papers on inequalities for harmonically convex functions. For some recent developments in integral inequalities and harmonical convexity, one can consult [16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

On Generalization of Different Integral Inequalities for Harmonically Convex Functions

et al. 2022

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In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers.

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Section: Introductionmentioning

confidence: 99%

On Generalization of Different Integral Inequalities for Harmonically Convex Functions

et al. 2022

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“…T. Sitthiwirattham et al, in the paper "On Some New Fractional Ostrowski-and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables" [8], proved three identities for functions of bounded variations. Then, by using these equalities, several trapezoid-and Ostrowski-type inequalities were obtained via generalized fractional integrals for the functions of bounded variations with two variables.…”

Section: Introductionmentioning

confidence: 99%

Special Issue Editorial “Symmetry in the Mathematical Inequalities”

Minculete

2022

Symmetry

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Some Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator

Nasir¹,

Qaisar²,

Butt³

et al. 2022

MATH

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<abstract><p>The comprehension of inequalities in preinvexity is very important for studying fractional calculus and its effectiveness in many applied sciences. In this article, we develop and study of fractional integral inequalities whose second derivatives are preinvex functions. We investigate and prove new lemma for twice differentiable functions involving Riemann-Liouville(R-L) fractional integral operator. On the basis of this newly developed lemma, we make some new results regarding of this identity. These new results yield us some generalizations of the prior results. This study builds upon on a novel new auxiliary result which enables us to develop new variants of Ostrowski type inequalities for twice differentiable preinvex mappings. As an application, several estimates concerning Bessel functions of real numbers are also illustrated.</p></abstract>

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On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables

Cited by 3 publications

References 38 publications

On Generalization of Different Integral Inequalities for Harmonically Convex Functions

On Generalization of Different Integral Inequalities for Harmonically Convex Functions

Special Issue Editorial “Symmetry in the Mathematical Inequalities”

Some Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator

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