Publication:
On some alpha-convex functions

Date
2008-06
Authors
Owa, Shigeyoshi
Polatoğlu, Yaşar
Yavuz, Emel
Acu, Mugur
Al-Oboudi, Fatima
Darus, Maslina
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Research Projects
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Abstract
In this paper, we define a general class of α-convex functions, denoted by MLβ,α(q), with respect to a convex domain D (q(z) ∈ Hu(U), q(0) = 1 , q(U) = D) contained in the right half plane by using the linear operator D β λ defined by D β λ : A → A , D β λ f(z) = z + X∞ j=2 (1 + (j − 1)λ) β ajz j , where β, λ ∈ R, β ≥ 0, λ ≥ 0 and f(z) = z+ X∞ j=2 ajz j . Regarding the class MLβ,α(q), we give a inclusion theorem and a transforming theorem, from which we may obtain many particular results.
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Keywords
α-convex functions, generalized Libera integral operator, BriotBouquet differential subordination, modified S˘al˘agean operator
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