Second and Third order differential subordination for exponential function

This article presents several findings regarding second and third-order differential subordination of the form: p(z)+γ₁ zp'(z)+γ₂ z²p''(z) h(z) p(z) eᶻ and p(z)+γ₁ zp'(z)+γ₂ z²p''(z)+γ₃ z³p'''(z) h(z) p(z) eᶻ. Here, γ₁, γ₂, and γ₃ represent positive real numbers, and various selections of $h(z)$ are explored within the context of the class S*ₑ := ∈ A : zf'(z)/f(z) eᶻ\, which denotes the class of starlike functions associated with the exponential function.