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We define and study the generalized unicorn problem in Finsler geometry. We mainly focus on regular (α, β)-metrics on an n-dimensional manifold M (n ≥ 3) in the form F = αϕ(β/α), where α= √aij(x)yiyj is a Riemannian metric and β = bi(x)yi is a 1-form on M. We prove that, if ϕ = ϕ(s) is a polynomial in s, then F = αϕ(β/α) is a weak Landsberg metric if and only if F is a Berwald metric. From this, we further prove that, if ϕ = ϕ(s) is a polynomial in s and αϕ(β/α) is not a Randers metric, then F is of relatively isotropic mean Landsberg curvature if and only if it is a Berwald metric. [ABSTRACT FROM AUTHOR]