  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.
