The authors obtain the Fekete-Szeg˝o inequality (according to parameters s and t in the region s 2 + st + t 2 < 3, s 6= t and s + t ≠ 2, or in the region s 2 + st + t 2 > 3, s 6= t and s + t 6= 2) for certain normalized analytic functions f(z) belonging to k-USTn λ,µ(s, t, γ) which satisfy the condition ℜ { (s − t)z(Dn λ,µf(z))′ ⁄ Dn λ,µf(sz) − Dn λ,µf(tz) } > k (s − t)z(Dn λ,µf(z))′ Dn λ,µf(sz) − Dn λ,µf(tz) −1 + γ, z ∈ U. Also certain applications of the main result a class of functions defined by the Hadamard product (or convolution) are given. As a special case of this result, the Fekete-Szegő inequality for a class of functions defined through fractional derivatives is obtained.