We consider radially symmetric m-subharmonic functions on the unit ball. We study their convexity and their relation with a solution of the complex Hessian equations. Furthermore, we consider the ordered vector space of radially symmetric m-subharmonic functions which is a Riesz space. Moreover, we shall define a space of m-subharmonic functions along with the Mabuchi metric. We also introduce a geodesic between two points in this space and give an equivalent condition when a curve on the space is geodesics. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.