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Dergiler / Turkish Journal of Mathematics / 2021 / Cilt: 45 - Sayı: 3

Fekete-Szegö problem for a new subclass of analytic functions satisfying subordinate condition associated with Chebyshev polynomials

Muhammet KAMALI
Mirzaolim TURABAEV
Erhan DENİZ
Murat ÇAĞLAR
Sayfa
1195–1208
Yayın Tarihi
2022-11-03
DOI
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The results presented in this paper improve the earlier investigations.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper,we define a class of analytic functions F(β,λ) (H, α, δ, µ), satisfying the following subordinate condition associated with Chebyshev polynomials   α [ zG′ (z) G (z) ]δ + (1 − α) [ zG′ (z) G (z) ]µ [ 1 + zG′′ (z) G ′ (z) ]1−µ    ≺ H (z, t), where G (z) = λβz2 f ′′ (z) + (λ − β) zf′ (z) + (1 − λ + β) f (z), 0 ≤ α ≤ 1, 1 ≤ δ ≤ 2, 0 ≤ µ ≤ 1, 0 ≤ β ≤ λ ≤ 1 and t ∈ ( 1 2 , 1 ] .
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Temel Bulgular & Veri:We obtain initial coefficients |a2| and |a3| for this subclass by means of Chebyshev polynomials expansions of analytic functions in D.
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Sonuç & Katkı:The results presented in this paper improve the earlier investigations.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper,we define a class of analytic functions F(β,λ) (H, α, δ, µ), satisfying the following subordinate condition associated with Chebyshev polynomials   α [ zG′ (z) G (z) ]δ + (1 − α) [ zG′ (z) G (z) ]µ [ 1 + zG′′ (z) G ′ (z) ]1−µ    ≺ H (z, t), where G (z) = λβz2 f ′′ (z) + (λ − β) zf′ (z) + (1 − λ + β) f (z), 0 ≤ α ≤ 1, 1 ≤ δ ≤ 2, 0 ≤ µ ≤ 1, 0 ≤ β ≤ λ ≤ 1 and t ∈ ( 1 2 , 1 ] . We obtain initial coefficients |a2| and |a3| for this subclass by means of Chebyshev polynomials expansions of analytic functions in D. Furthermore, we solve Fekete-Szegö problem for functions in this subclass.We also provide relevant connections of our results with those considered in earlier investigations. The results presented in this paper improve the earlier investigations.

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Bu Makaleye Atıf Yap

KAMALI, M., TURABAEV, M., DENİZ, E., ÇAĞLAR, M. (2022). Fekete-Szegö problem for a new subclass of analytic functions satisfying subordinate condition associated with Chebyshev polynomials. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 3, 1195–1208. https://ajindex.com/articles/607468

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