Fractional Integral Estimates of Hermite-Hadamard type in Global Nonpositive Curvature Spaces

Abstract

We extend the notion of convexity of functions defined on global nonpositive curvature spaces by introducing (geodesically) $h$-convex functions. We prove estimates of Hermite-Hadamard type via Katugampola's fractional integrals. We obtain an important corollary which gives an essentially sharp estimate involving squared distance mappings between points in a global NPC space. This is a contribution to analysis on spaces with curved geometry.