Gamma-Bazilevi? Functions

Sa’adatul Fitri and Derek K. Thomas
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Sa’adatul Fitri: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Jl. Veteran, Malang 65145, East Java, Indonesia
Derek K. Thomas: Department of Mathematics, Swansea University, Bay Campus, Swansea SA1 8EN, UK

Mathematics, 2020, vol. 8, issue 2, 1-8

Abstract: For γ ≥ 0 and α ≥ 0 , we introduce the class B 1 γ ( α ) of Gamma–Bazilevi? 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 ) Bazilevi? functions, and is therefore univalent in D . Various coefficient problems for functions in B 1 γ ( α ) are also given.

Keywords: univalent; Bazilevi? functions; coefficients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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