The Fekete–Szegö functional associated with m -th root transformation using conical domains

UDC 517.5 Let 𝒜 be the class of analytic functions in the open unit disk 𝕌 = { z ∈ ℂ : | z | < 1 } . Let ℛ α p be the operator defined on 𝒜 by ℛ α p = f ( z ) * z ( 1 - z ) 2 ( 1 - α ) . A function f in 𝒜 is said to be in the class k - S P α p if ℛ α p ( f ) is a k -parabolic starlike function. We focus on the Fekete–Szegö inequality associated with m -th root transformation using conical domains for this class.