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FRACTIONAL TRAPEZOID AND NEWTON TYPE INEQUALITIES FOR DIFFERENTIABLE S-CONVEX FUNCTIONS
Fatih Hezenci,Huseyin Budak,Muhammad Aamir Ali 호남수학회 2023 호남수학학술지 Vol.45 No.1
In the present paper, we prove that our main inequality reduces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the wellknown Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.
Fatih Hezenci,Huseyin Budak 강원경기수학회 2023 한국수학논문집 Vol.31 No.2
In this paper, an equality is established by twice-differentiable convex functions with respect to the conformable fractional integrals. Moreover, several Simpson-type inequalities are presented for the case of twice-differentiable convex functions via conformable fractional integrals by using the established equality. Furthermore, our results are provided by using special cases of obtained theorems.
( Fatih Hezenci ),( Hüseyin Budak ) 호남수학회 2023 호남수학학술지 Vol.45 No.2
This article establishes an equality for the case of twicedifferentiable convex functions with respect to the conformable fractional integrals. With the help of this identity, we prove sundry midpointtype inequalities by twice-differentiable convex functions according to conformable fractional integrals. Several important inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Using the specific selection of our results, we obtain several new and well-known results in the literature.
PERTURBED FRACTIONAL NEWTON-TYPE INEQUALITIES BY TWICE DIFFERENTIABLE FUNCTIONS
( Fatih Hezenci ),( Hasan Kara ),( Hüseyin Budak ) 호남수학회 2023 호남수학학술지 Vol.45 No.2
In the present paper, we establish some perturbed Newtontype inequalities in the case of twice differentiable convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the aid of special cases of our main results, we also give some previously obtained Newton-type inequalities.