On gMT- and gβ-convexity and the Ostrowski type inequalities

In this study, motivated by recent results on Ostrowski-type inequalities, we introduce a new identity that serves as a basis for establishing fractional Ostrowski inequalities. Specifically, we focus on functions whose modulus of the first derivatives are gMT-convex and gβ-convex. This approach allows us to extend classical results to more general settings. Several special cases are discussed, recovering known inequalities while highlighting the versatility of our method.