Hermite–Hadamard-type Inequalities for $$\hbar$$ ħ -preinvex Interval-Valued Functions via Fractional Integral

Abstract

Abstract We present a comprehensive study on Hermite–Hadamard-type inequalities for interval-valued functions that are $$\hbar$$ ħ -preinvex, using the Riemann–Liouville fractional integral. Our research extends and generalizes some existing results found in the literature. In addition, we provide accurate proofs for the main theorems originally derived by Srivastava et al. in their publication titled “Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators" (Int. J. Comput. Int. Sys. 15(1):8, 2022). Finally, we illustrate our findings through a practical example to demonstrate the validity of our results.

Keywords

• $$\hbar$$ ħ -Preinvex functions
• Interval-valued functions
• Riemann–Liouville fractional integral
• Hermite–Hadamard inequalities