Some results on a starlike log-harmonic mapping of order alpha
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Dosyalar
Tarih
2014-01-15
Yazarlar
Dergi Başlığı
Dergi ISSN
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Yayıncı
Elsevier Science BV
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let H(D) be the linear space of all analytic functions defined on the open unit disc D = z is an element of C : vertical bar z vertical bar < 1. A sense preserving log-harmonic mapping is the solution of the non-linear elliptic partial differential equation f(z) = w(z)f(z)(f(z)/f) where w(z) is an element of H (D) is the second dilatation off such that vertical bar w(z)vertical bar < 1 for all z is an element of D.A sense preserving log-harmonic mapping is a solution of the non-linear elliptic partial differential equation fz f((z) over bar)/(f) over bar = w(z).f(z)/f (0.1) where w(z) the second dilatation off and w(z) is an element of H(D), vertical bar w(z)vertical bar < 1 for every z is an element of D. It has been shown that if f is a non-vanishing log-harmonic mapping, then f can be expressed as f(z) = h(z)<(g(z))over bar> (0.2) where h(z) and g(z) are analytic in D with the normalization h(0) not equal 0, g(0) = 1. On the other hand if f vanishes at z = 0, but it is not identically zero, then f admits the following representation f(z) = z.z(2 beta)h(z)<(g(z))over bar> (0.3) where Re beta > -1/2, h(z) and g(z) are analytic in the open disc D with the normalization h(0) not equal 0, g(0) = 1 (Abdulhadi and Bshouty, 1988) [2], (Abdulhadi and Hengartner, 1996) [3].In the present paper, we will give the extent of the idea, which was introduced by Abdulhadi and Bshouty (1988) [2]. One of the interesting applications of this extent idea is an investigation of the subclass of log-harmonic mappings for starlike log-harmonic mappings of order alpha.
Açıklama
Anahtar Kelimeler
Log-harmonic mappings, Starlike function, Distortion theorem, Analytic functions, Distortion theorems, Elliptic partial differential equation, Linear spaces, Starlike functions, Unit disc, Partial differential equations, Harmonic functions
Kaynak
Journal of Computational and Applied Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
256
Sayı
Künye
Aydoğan, S. M. (2014). Some results on a starlike log-harmonic mapping of order alpha. Journal of Computational and Applied Mathematics, 256, 77-82. doi:10.1016/j.cam.2013.07.008
