Integral Inequalities Using Generalized Convexity Property Pertaining to Fractional Integrals and Their Applications

Abstract

In this study, we established the Hermite-Hadamard type, Simpson type, Ostrowski type and midpoint type integral inequalities for the s-convex functions in the second sense via Katugampola fractional integrals. By using Katugampola fractional integral operators, we obtained several new identities and presented new results for the s-convex function in the second sense. We made connections of our results with various results recognized in the literature. Finally, applications to special means are examined to verify the efficiency of the established results.

Keywords

• hermite-hadamard type inequalities
• simpson type inequalities
• ostrowski type inequalities
• holder's inequality
• young's inequality
• s-convex function
• katugampola fractional integral operators
• special means