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Open AccessFeature PaperArticle

Gamma-Bazilevič Functions

1
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Jl. Veteran, Malang 65145, East Java, Indonesia
2
Department of Mathematics, Swansea University, Bay Campus, Swansea SA1 8EN, UK
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 175; https://doi.org/10.3390/math8020175
Received: 6 January 2020 / Revised: 28 January 2020 / Accepted: 29 January 2020 / Published: 2 February 2020
(This article belongs to the Special Issue Complex Analysis and Its Applications 2019)
For γ 0 and α 0 , we introduce the class B 1 γ ( α ) of Gamma–Bazilevič functions defined for z D by R e z f ( z ) f ( z ) 1 - α z α + z f ( z ) f ( z ) + ( α - 1 ) z f ( z ) f ( z ) - 1 γ z f ( z ) f ( z ) 1 - α z α 1 - γ > 0 . We shown that B 1 γ ( α ) is a subset of B 1 ( α ) , the class of B 1 ( α ) Bazilevič functions, and is therefore univalent in D . Various coefficient problems for functions in B 1 γ ( α ) are also given.
Keywords: univalent; Bazilevič functions; coefficients univalent; Bazilevič functions; coefficients
MDPI and ACS Style

Fitri, S.; Thomas, D.K. Gamma-Bazilevič Functions. Mathematics 2020, 8, 175.

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