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Further refinements and inequalities of Fejer's type via GA-convexity
(Ramazan Yaman, 2024) Latif, Muhammad Amer; Budak, Hüseyin; Kashuri, Artion
In this study, we introduce some new mappings in connection with HermiteHadamard and Fejer type integral inequalities which have been proved using the GA-convex functions. As a consequence, we obtain certain new inequalities of the Fejer type that provide refinements of the Hermite-Hadamard and Fejer type integral inequalities that have already been obtained.
Hermite-Hadamard-Type Inequalities Arising from Tempered Fractional Integrals Including Twice-Differentiable Functions
(Springer, 2025) Hezenci, Fatih; Budak, Hueseyin; Latif, Muhammad Amer
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 H & ouml;lder 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.