On Hermite-Hadamard type inequalities of coordinated (p1,h1)-(p2,h2)-convex functions via Katugampola fractional integrals

Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.

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“…The above inequalities have attracted many researchers in the recent years, see e.g. [34][35][36][37][38].…”

Section: Definition 22 ([32]mentioning

confidence: 99%

General Raina fractional integral inequalities on coordinates of convex functions

et al. 2021

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New fractional integral inequalities pertaining 2D–approximately coordinate (r1,ℏ1)-(

Song

Butt

Kashuri

et al. 2022

Alexandria Engineering Journal

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New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas

et al. 2022

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In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained.

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On Hermite-Hadamard type inequalities of coordinated (p1,h1)-(p2,h2)-convex functions via Katugampola fractional integrals

Cited by 5 publications

References 12 publications

General Raina fractional integral inequalities on coordinates of convex functions

General Raina fractional integral inequalities on coordinates of convex functions

New fractional integral inequalities pertaining 2D–approximately coordinate (r1,ℏ1)-(

New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas

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