New Inequalities for Differentiable Mappings via Fractional Integral Operators (European Journal of Pure and Applied Mathematics, 2025)
In this study, explicit bounds for the midpoint type inequalities for functions whose twice differentiable in absolute value raised to positive real powers are $(ρ, s)$ and $(ρ, s, m)$-convexities are explored through the integral fractional operator. Several estimate for special functions including Euler gamma, incomplete Beta and hypergeometric functions are presented in the study.
Keywords: Riemann-Liouville integrals; H\"older's inequality; Integral inequality; $(ρ, s, m)$-convex functions.