Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities

Abstract

We propose the concept of up and down harmonically convex mapping for fuzzy-number-valued mapping as our main goal in this work. With the help of up and down harmonically fuzzy-number convexity and the fuzzy fractional integral operator, we also show the results for the Hermite–Hadamard (H–H) inequality, the Fejér type inequality, and some other related versions of inequalities. Moreover, some examples are also presented to discuss the validity of the main results. The results from the new technique show how the suggested scheme is accurate, adaptable, efficient, and user-friendly.

Keywords

• up and down harmonically convex fuzzy-number-valued function
• fuzzy fractional integral Hermite–Hadamard inequality
• Hermite–Hadamard–Fejér inequality