Integral inequalities for s-convex functions via generalized conformable fractional integral operators

• Main Authors: Artion Kashuri, Sajid Iqbal, Rozana Liko, Wei Gao, Muhammad Samraiz
• Format: Article
• Language: English
• Published: SpringerOpen 2020-05-01
• Series: Advances in Difference Equations
• Subjects: Hermite–Hadamard inequality; Hölder inequality; Power mean inequality; Convexity; Conformable fractional integral; General fractional integral operators
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02671-4
• ISSN: 1687-1847

Abstract We introduce new operators, the so-called left and right generalized conformable fractional integral operators. By using these operators we establish new Hermite–Hadamard inequalities for s-convex functions and products of two s-convex functions in the second sense. Also, we obtain two interesting identities for a differentiable function involving a generalized conformable fractional integral operator. By applying these identities we give Hermite–Hadamard and midpoint-type integral inequalities for s-convex functions. Different special cases have been identified and some known results are recovered from our general results. These results may motivate further research in different areas of pure and applied sciences.