a new subclass of ma-minda starlike functions associated with a heart-shaped curve

In this paper, we extend the q-derivative operator, which plays an essential role in quantum calculus. indeed, by using the hadamard product and generalized koebe function we define the following (α, β, γ)-derivative operator dα,β,γf(z) = 1/z {f(z) ∗ lα,β,γ(z)} , where lα,β,γ(z) = 2(1 − γ)z/(1 − αz)(1 − βz), and α ∈ [−1, 1], β ∈ [−1, 1], αβ ̸= ±1 and γ ∈ [0, 1). then by subordination relation, the operator dα,β,γf(z), and a special function ϕδ(z) = 1 + δz/ exp(δz) (0 < δ ≤ 1), we define a new particular ma-minda class. we investigate some properties of this class, such as, radius problem and coefficient estimate.