Hermite–Hadamard-type inequalities arising from tempered fractional integrals including twice-differentiable functions

Fatih Hezenci; Hüseyin Budak; Muhammad Amer Latif

doi:10.3842/umzh.v76i9.7640

Fatih Hezenci Department of Mathematics, Faculty of Science and Arts, Duzce University, Turkey https://orcid.org/0000-0003-1008-5856
Hüseyin Budak Department of Mathematics, Faculty of Science and Arts, Duzce University, Turkey
Muhammad Amer Latif Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Al-Hasa, Saudi Arabia

DOI: https://doi.org/10.3842/umzh.v76i9.7640

Keywords: Hermite--Hadamard-type inequalities, convex functions, fractional integrals, tempered fractional integrals

Abstract

UDC 517.5

We propose a new method for the investigation of integral identities according to tempered fractional operators. In addition, we prove the midpoint-type and trapezoid-type inequalities by using twice-differentiable convex functions associated with tempered fractional integral operators. We use the well-known Hölder inequality and the power-mean inequality in order to obtain inequalities of these types. The resulting Hermite–Hadamard-type inequalities are generalizations of some investigations in this field, involving Riemann–Liouville fractional integrals.

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