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Fekete-Szego inequality of bi-starlike and bi-convex functions of order b associated with symmetric q-derivative in conic domains

", Bharavi Sharma Rayaprolu, Rajya Laxmi Kalikota, N. Magesh · 2022 📄 DOI →

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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)

Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.

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:
bi-univalent

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