Abstract
Sharp bounds for the Fekete-Szegö functional |ν_1-ξ〖ν_0〗^2 | are derived for certain class of meromorphic starlike functions ω(z) of order β defined on the punctured open unit disk for which 1-1/t ((D^(n+1˳m) ω(z))/(D^(n˳m) ω(z) )-1)≺χ(z) (t∈C-{0},η≥0,κ>0,n,m∈N_0), lie in a region starlike with respect to 1 and symmetric with respect to the real axis.
Highlights
Let Ʃ denote the class of meromorphic functions of the form
In the class ;∗ and Ʃ∗ that introduced and studied respectively by Ma and Minda [8], Silverman et al [3], the authors have obtained the Fekete-Szegö inequality for the functions in these classes. In this present paper we consider the operator defined by El-Ashwah [7]
The result is sharp for the functions: 1−
Summary
In the class ;∗ and Ʃ∗ that introduced and studied respectively by Ma and Minda [8], Silverman et al [3], the authors have obtained the Fekete-Szegö inequality for the functions in these classes. In this present paper we consider the operator defined by El-Ashwah [7]. Let be an analytic function with positive real part on -∗ with 0 = 1, ′ 0 > 1 which maps the unit disk - onto a region of -starlike with respect to 1 and is symmetric with respect to the real axis.
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