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 [[phi].sub.k]-Riemann-Liouville ([[phi].sub.k] - RL) fractional integrals. Also, several inequalities using extended operations on the newly defined class of convex IV functions are given. Keywords: H * H inequality; [[phi].sub.k]--RL fractional integrals; IV convex function Mathematics Subject Classification: 26A51, 26A33, 26D07, 26D10, 26D15