2019
DOI: 10.1007/s00025-019-1030-y
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Coefficient Problems in the Subclasses of Close-to-Star Functions

Abstract: For two subclasses of close-to-star functions we estimate early logarithmic coefficients, coefficients of inverse functions, Hankel determinant H2,2 and Zalcman functional J2,3. All results are sharp. Mathematics Subject Classification. 30C45. Keywords. Univalent functions, close-to-star functions, functions starlike in the direction of the real axis, functions convex in the direction of the imaginary axis, Hankel determinant, Zalcman functional, logarithmic coefficients, inverse functions, Carathéodory class.… Show more

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Cited by 10 publications
(6 citation statements)
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“…See [2,7,14,15,33]. Also, in 2019, Lecko and Sim [20] considered two functions Φ(z) = 1/(1 − z) 2 , 1/(1 − z 2 ) where zΦ(z) are starlike functions with integer coefficients and studied on Re f (z)/(zΦ(z)) > 0. Similar studies can be seen in [16][17][18].…”
Section: Introductionmentioning
confidence: 99%
“…See [2,7,14,15,33]. Also, in 2019, Lecko and Sim [20] considered two functions Φ(z) = 1/(1 − z) 2 , 1/(1 − z 2 ) where zΦ(z) are starlike functions with integer coefficients and studied on Re f (z)/(zΦ(z)) > 0. Similar studies can be seen in [16][17][18].…”
Section: Introductionmentioning
confidence: 99%
“…Each electrode extracted three sets of characteristics: sixth-order AR coefficients, spectral density, and total power in five frequency bands. Six AR coefficients were used as proposed for EEG classification in [27]. Specifically, biologically significant bands and spectral powers were used to obtain brain activity.…”
Section: Machine Learning Referencesmentioning
confidence: 99%
“…Recently, Lecko et al [14] investigated the classes Re(1 − z 2 )f (z)/z > 0 and Re(1 − z) 2 f (z)/z > 0, involving the starlike functions z/(1 − z 2 ) and z/(1 − z) 2 . In 2019, Cho et al [5] estimated radii constants for classes characterised by the ratio of two analytic functions f (z) and g(z) along with some conditions associated with g(z), namely Re g(z)/z > α where α = 0 or 1/2, such that Re f (z)/g(z) > 0.…”
Section: Radius Problemsmentioning
confidence: 99%