Mohammed, Pshtiwan OthmanSarıkaya, Mehmet Zeki2020-05-012020-05-0120181029-242Xhttps://doi.org/10.1186/s13660-018-1950-1https://hdl.handle.net/20.500.12684/6142Mohammed, Pshtiwan/0000-0001-6837-8075WOS: 000454541600002PubMed: 30839932In this study, the family F and F-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite-Hadamard type for differentiable function. Moreover, we establish some trapezoid type inequalities for functions whose second derivatives in absolute values are F-convex. We also show that through the notion of F-convex we can find some new Hermite-Hadamard type and trapezoid type inequalities for the Riemann-Liouville fractional integrals and classical integrals.en10.1186/s13660-018-1950-1info:eu-repo/semantics/openAccessF-convexlambda(phi)-preinvexIntegral inequalitiesArticleWOS:000454541600002Q2Q1