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Hankel Determinants for New Subclasses of Analytic Functions Related to a Shell Shaped Region

1
Department of Mathematics, SAS, Vellore Institute of Technology, Deemed to be University, Vellore 632014, India
2
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
*
Author to whom correspondence should be addressed.
Dedicated to the memory of Professor Stephan Ruscheweyh 1944–2019.
These authors contributed equally to this work.
Mathematics 2020, 8(6), 1041; https://doi.org/10.3390/math8061041
Received: 25 May 2020 / Revised: 23 June 2020 / Accepted: 24 June 2020 / Published: 26 June 2020
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory)
Using the operator L c a defined by Carlson and Shaffer, we defined a new subclass of analytic functions ML c a ( λ ; ψ ) defined by a subordination relation to the shell shaped function ψ ( z ) = z + 1 + z 2 . We determined estimate bounds of the four coefficients of the power series expansions, we gave upper bound for the Fekete–SzegőSzegő functional and for the Hankel determinant of order two for f ML c a ( λ ; ψ ) . View Full-Text
Keywords: analytic functions; Hadamard (convolution) product; Carathéodory functions; Hankel determinant; Fekete–Szegő problem; Carlson–Shaffer operator; differential subordination analytic functions; Hadamard (convolution) product; Carathéodory functions; Hankel determinant; Fekete–Szegő problem; Carlson–Shaffer operator; differential subordination
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Murugusundaramoorthy, G.; Bulboacă, T. Hankel Determinants for New Subclasses of Analytic Functions Related to a Shell Shaped Region. Mathematics 2020, 8, 1041.

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