Atıf İçin Kopyala
Dorff M., Hamidi S. G., Jahangiri J. M., Yaar E.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, cilt.66, sa.11, ss.1904-1921, 2021 (SCI-Expanded)
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Yayın Türü:
Makale / Tam Makale
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Cilt numarası:
66
Sayı:
11
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Basım Tarihi:
2021
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Doi Numarası:
10.1080/17476933.2020.1789864
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Dergi Adı:
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
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Derginin Tarandığı İndeksler:
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, Civil Engineering Abstracts
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Sayfa Sayıları:
ss.1904-1921
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Anahtar Kelimeler:
Convolutions, planar harmonic mappings, directional convexity
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Bursa Uludağ Üniversitesi Adresli:
Evet
Özet
We consider classes of harmonic univalent functions f(k) = h(k) + (g) over bar (k), (k = 1, 2) that are shears of the analytic map h(k) - g(k) = 1/2 log[(1 + z) / (1 - z)] with dilatation omega(k) = e(i theta k) z(k). We prove that if the convolution f(1) * f(2) is locally one-to-one and sense-preserving, then f(1) * f(2) is convex in the direction of the real axis.