In this paper, we introduce a new class of Finsler metrics that generalize the well-known (α,β)-metrics.
These metrics are defined by a Riemannian metric α and two 1-forms β=bi(x)yi and γ=γi(x)yi.
This new class of metrics not only generalizes (α,β)-metrics, but also includes other important Finsler metrics,
such as all (generalized) γ-changes of generalized (α,β)-metrics, (α,β)-metrics, and spherically symmetric Finsler metrics in Rn.
We find a necessary and sufficient condition for this new class of metrics to be locally projectively flat.
Furthermore, we prove the conditions under which these metrics are of Douglas type.
Keywords: Finsler geometry, (α,β,γ)-metrics, Projectively flat, Douglas space.