In this paper, we derive various distortion theorems for the fractional calculus and the fractional integral operator of the function h, the analytic part of the function f, if the function f belongs to the class TH(α, β).
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Recently, Jahangiri [4] studied the harmonic starlike functions of order α, and he defined the class TH(α) consisting of functions f = h + g¯, where h and g are the analytic and the co-analytic part of the function f, respectively.
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Temel Bulgular & Veri:In [3] the author introduced the class TH(α, β) of analytic functions and he proved various coefficient inequalities and growth and distortion theorems, and obtained the radius of convexity for the function h if the function f belongs to the classes TH(α) and TH(α, β).
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Sonuç & Katkı:In this paper, we derive various distortion theorems for the fractional calculus and the fractional integral operator of the function h, the analytic part of the function f, if the function f belongs to the class TH(α, β).
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Harmonic · Analytic and univalent functions · Fractional calculus and fractional integral operator
Abstract
Recently, Jahangiri [4] studied the harmonic starlike functions of order α, and he defined the class TH(α) consisting of functions f = h + g¯, where h and g are the analytic and the co-analytic part of the function f, respectively. In [3] the author introduced the class TH(α, β) of analytic functions and he proved various coefficient inequalities and growth and distortion theorems, and obtained the radius of convexity for the function h if the function f belongs to the classes TH(α) and TH(α, β). In this paper, we derive various distortion theorems for the fractional calculus and the fractional integral operator of the function h, the analytic part of the function f, if the function f belongs to the class TH(α, β).
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