Relations of a planar domains bounded by hyperbolas with families of holomorphic functions

In the current paper, we study a majorization issue for a general category S * ( ϑ ) of starlike functions, the region of which is often symmetric with respect to the real axis. For various special symmetric functions ϑ , corresponding consequences of the main result are also presented with some relevant connections of the outcomes rendered here with those obtained in recent research. Moreover, coefficient bounds for some majorized functions are estimated.

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“…The following corollary concludes a majorization property for the subclass ST hpl (b) considering Lemma 2.1 in [9]. Corollary 1.…”

Section: Remarkmentioning

confidence: 69%

“…Lately, Kanas et al [9] defined the class ST hpl (b) := S * (q b (z)) and obtained some geometric properties in this class where the function…”

Section: Introductionmentioning

confidence: 99%

Majorization and Coefficient Problems for a General Class of Starlike Functions

et al. 2020

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“…According to the inequality (20) of [12] (Theorem 2.3), the function q 1/2 is analytic with positive real part in U. Therefore, using [27] (Theorem 1) for β = 1, γ = 0, and c = 1, it follows that the solution p of the differential equation (44) is analytic in U with Re pðzÞ > 0, z ∈ U, and The plot of ΨðRe it Þ for t ∈ ½0, 2πÞ, R = 1, and α ∈ ð10 −6 , 1.…”

Section: Journal Of Function Spacesmentioning

confidence: 99%

“…and plays as extremal function for some extremal problems in the set Cð1 + αzÞ. Lately, Kanas et al [12] introduced the categories S T hpl ðsÞ and CV hpl ðsÞ by…”

Section: Introductionmentioning

confidence: 99%

Logarithmic Coefficient Bounds and Coefficient Conjectures for Classes Associated with Convex Functions

Alimohammadi

Adegani

Bulboacă

et al. 2021

Journal of Function Spaces

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It is well-known that the logarithmic coefficients play an important role in the development of the theory of univalent functions. If S denotes the class of functions f z = z + ∑ n = 2 ∞ a n z n analytic and univalent in the open unit disk U , then the logarithmic coefficients γ n f of the function f ∈ S are defined by log f z / z = 2 ∑ n = 1 ∞ γ n f z n . In the current paper, the bounds for the logarithmic coefficients γ n for some well-known classes like C 1 + α z for α ∈ 0 , 1 and C V hpl 1 / 2 were estimated. Further, conjectures for the logarithmic coefficients γ n for functions f belonging to these classes are stated. For example, it is forecasted that if the function f ∈ C 1 + α z , then the logarithmic coefficients of f satisfy the inequalities γ n ≤ α / 2 n n + 1 , n ∈ ℕ . Equality is attained for the function L α , n , that is, log L α , n z / z = 2 ∑ n = 1 ∞ γ n L α , n z n = α / n n + 1 z n + ⋯ , z ∈ U .

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“…For various choices of ψ and a detailed discussion about classes we refer to the papers [5][6][7][8][9].…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

Subclasses of Starlike and Convex Functions Associated with the Limaçon Domain

Masih

Kanas

2020

Symmetry

Self Cite

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Let ST L ( s ) and CV L ( s ) denote the family of analytic and normalized functions f in the unit disk D : = z : | z | < 1 , such that the quantity z f ′ ( z ) / f ( z ) or 1 + z f ″ ( z ) / f ′ ( z ) respectively are lying in the region bounded by the limaçon ( u − 1 ) 2 + v 2 − s 4 2 = 4 s 2 u − 1 + s 2 2 + v 2 , where 0 < s ≤ 1 / 2 . The limaçon of Pascal is a curve that possesses properties which qualify it for the several applications in mathematics, statistics (hypothesis testing problem) but also in mechanics (fluid processing applications, known limaçon technology is employed to extract electrical power from low-grade heat, etc.). In this paper we present some results concerning the behavior of f on the classes ST L ( s ) or CV L ( s ) . Some appropriate examples are given.

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Relations of a planar domains bounded by hyperbolas with families of holomorphic functions

Cited by 21 publications

References 6 publications

Majorization and Coefficient Problems for a General Class of Starlike Functions

Majorization and Coefficient Problems for a General Class of Starlike Functions

Logarithmic Coefficient Bounds and Coefficient Conjectures for Classes Associated with Convex Functions

Subclasses of Starlike and Convex Functions Associated with the Limaçon Domain

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