On modified convex interval valued functions and related inclusions via the interval valued generalized fractional integrals in extended interval space

In this paper, we propose a new family of interval valued (IV) convex functions termed as generalized modified $ (p, h) $-convex IV functions. We obtain the counterpart of Hermite-Hadamard H· H inequality by extending the IV fractional integral to the IV \; ψₖ-Riemann-Liouville (ψₖ-RL) fractional integrals. Also, several inequalities using extended operations on the newly defined class of convex IV functions are given.