Some New Integral Inequalities for Generalized Preinvex Functions in Interval-Valued Settings

Abstract

In recent years, there has been a significant amount of research on the extension of convex functions which are known as preinvex functions. In this paper, we have used this approach to generalize the preinvex interval-valued function in terms of (£1, £2)-preinvex interval-valued functions because of its extraordinary applications in both pure and applied mathematics. The idea of (£1, £2)-preinvex interval-valued functions is explained in this work. By using the Riemann integral operator, we obtain Hermite-Hadamard and Fejér-type inequalities for (£1, £2)-preinvex interval-valued functions. To discuss the validity of our main results, we provide non-trivial examples. Some exceptional cases have been discussed that can be seen as applications of main outcomes.

Keywords

• interval-valued functions
• fuzzy Riemann integrals
• (<i>£</i>₁, <i>£</i>₂)-preinvex interval-valued functions
• Hermite-Hadamard inequalities