On (α,β)-Metrics with Reversible Geodesics

In this paper,we get necessary and sufficient conditions for a Finsler space endowed with an(α,β)-metric where its geodesic coefficients G~i(x,y) and the reverse of geodesic coefficients G~i(x,-y) have the same Douglas curvature.They are the conditions such that(α,β)-metrics have reversible geodesics.