@article{Hezenci_Budak_Latif_2024, title={Hermite–Hadamard-type inequalities arising from tempered fractional integrals including twice-differentiable functions}, volume={76}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/7640}, DOI={10.3842/umzh.v76i9.7640}, abstractNote={<p>UDC 517.5</p> <p>We propose a new method for the investigation of integral identities according to tempered fractional operators.<span class="Apple-converted-space"> </span>In addition, we prove the midpoint-type and trapezoid-type inequalities by using twice-differentiable convex functions associated with tempered fractional integral operators.<span class="Apple-converted-space"> </span>We use the well-known Hölder inequality and the power-mean inequality in order to obtain inequalities of these types.<span class="Apple-converted-space"> </span>The resulting Hermite–Hadamard-type inequalities are generalizations of some investigations in this field, involving Riemann–Liouville fractional integrals.</p>}, number={9}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Hezenci, Fatih and Budak, Hüseyin and LatifMuhammad Amer}, year={2024}, month={Sep.}, pages={1395 - 1411} }