On Estimates of Some Coefficient Functionals for Certain Meromorphic Univalent Functions

Let V p ( λ ) be the class of all functions f defined on the open unit disc D of the complex plane having simple pole at z = p , p ∈ ( 0 , 1 ) and analytic in D \ { p } satisfying the normalizations f ( 0 ) = 0 = f ′ ( 0 ) - 1 such that ( z / f ( z ) ) 2 f ′ ( z ) - 1 < λ for z ∈ D , λ ∈ ( 0 , 1...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2022-09, Vol.45 (5), p.2745-2763
Main Authors: Bhowmik, Bappaditya, Parveen, Firdoshi
Format: Article
Language:English
Subjects:
Applications of Mathematics
Functionals
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary:Let V p ( λ ) be the class of all functions f defined on the open unit disc D of the complex plane having simple pole at z = p , p ∈ ( 0 , 1 ) and analytic in D \ { p } satisfying the normalizations f ( 0 ) = 0 = f ′ ( 0 ) - 1 such that ( z / f ( z ) ) 2 f ′ ( z ) - 1 < λ for z ∈ D , λ ∈ ( 0 , 1 ] . In this article, we obtain sharp bounds of the Zalcman and the generalized Zalcman functionals for functions in V p ( λ ) for some indices of these functionals. As consequences of the obtained results, we pose the Zalcman-like coefficient conjectures for this class of functions. In addition, we estimate bound for the generalised Fekete–Szegö functional along with bounds of the second- and the third-order Hankel determinants for this class of functions.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-022-01309-w