New Hermite–Hadamard Inequalities Concerning Twice Differentiable Generalized ψ-Convex Mappings via Conformable Fractional Integrals

Abstract

AbstractIn this article, we first introduced a new class of generalized ((p1, p2);(ψ1, ψ2))–convex mappings and an interesting lemma regarding Hermite–Hadamard type conformable fractional integral inequalities. By using the notion of generalized ((p1, p2);(ψ1, ψ2))–convexity and lemma as an auxiliary result, some new estimates with respect to Hermite–Hadamard type integral inequalities associated with twice differentiable generalized ((p1, p2);(ψ1, ψ2))–convex mappings via conformable fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article. At the end, some applications to special means are also given.KeywordsHermite–Hadamard inequalityHölder’s inequalityMinkowski inequalityPower mean inequalityConformable fractional integrals m-invex2010 Mathematics Subject ClassificationPrimary: 26A51; Secondary: 26A3326D0726D1026D15