Abstract
The main purpose of the present paper is to derive the neighborhoods and partial sums of a certain subclass of starlike functions. MSC: 30C45.
Highlights
Let Am denote the class of functions f of the form ∞ f (z) = z +akzk m ∈ N := {, . . .}, ( . ) k=m+which are analytic in the open unit diskU := z : z ∈ C and |z| < .A function f ∈ Am is said to be in the class Sm∗ (β) of starlike functions of order β if it satisfies the inequality zf (z) >β (z ∈ U; β < ). f (z)
Assuming that α, β < and f ∈ Am, we say that a function f ∈ Hm(α, β) if it satisfies the condition zf (z) z f (z) +α m mα
For some recent investigations involving the partial sums in analytic function theory, one can refer to [ – ] and the references cited therein
Summary
Abstract The main purpose of the present paper is to derive the neighborhoods and partial sums of a certain subclass of starlike functions. Introduction Let Am denote the class of functions f of the form A function f ∈ Am is said to be in the class Sm∗ (β) of starlike functions of order β if it satisfies the inequality zf (z) >β
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