Stud. Univ. Babe¸s-Bolyai Math. 67(2022), No. 3, 475–487

Abstract

In this paper, two new subclasses of bi-univalent functions related to conic domains are deﬁned by making use of symmetric q-diﬀerential operator. The initial bounds for Fekete-Szeg¨o inequality for the functions f in these classes are estimated. Mathematics Subject Classiﬁcation (2010): 30C45, 30C50.

Results & Lemmas (2)

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Theorem 2.1. Theorem 2.1. If f ∈k −S T Σ, b(α, β) and is of the form (1.1) then |a2| ≤ |P1| p |P1|b2 r |P 2 1 b f [3]q −f [2]q + 2(P1 −P2) f [2]q −1

Theorem 2.1. If f ∈k −S T Σ, b(α, β) and is of the form (1.1) then |a2| ≤ |P1| p |P1|b2 r |P 2 1 b f [3]q −f [2]q + 2(P1 −P2) f [2]q −1

Theorem 2.2. Theorem 2.2. If f ∈k −U C V Σ, b(α, β) and is of the form (1.1), then |a2| ≤ |P1| |b| p |P1| s f [3]q f [3]q −1 −f [2] 2

Theorem 2.2. If f ∈k −U C V Σ, b(α, β) and is of the form (1.1), then |a2| ≤ |P1| |b| p |P1| s f [3]q f [3]q −1 −f [2] 2

Function classes studied:

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Stud. Univ. Babe¸s-Bolyai Math. 67(2022), No. 3, 475–487

Results & Lemmas (2)

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