Coefficient Bounds for Certain Classes of Meromorphic Functions

Silverman, Herb; Suchithra, K.; Stephen, B. Adolf; Gangadharan, A.

doi:10.1155/2008/931981

Cited by 13 publications

(8 citation statements)

References 7 publications

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“…Corollary 5. For φðωÞ = 1 and γ = 0 in Theorem 4, we obtain the result by Silverman et al [3] (see Theorem 4).…”

Section: Resultssupporting

confidence: 84%

“…Corollary 8. For φðωÞ = 1, δðωÞ = λðωÞ, and η = 0 in Theorem 7, we obtain the result by Silverman et al [3] (see Theorem 7). For kðωÞ = ω and repeating steps of Theorem 7, we obtain the following corollary.…”

Section: Corollary 6 Let λðωþsupporting

confidence: 81%

“…In our present investigation, we have defined and systematically studied the famous Fekete-szego inequality for some subclass of meromorphic functions by using quasisubordination. It is important to mention that certain results in the literature, for example [3,19,20], are special cases of the results obtained by us.…”

Section: Journal Of Function Spacesmentioning

confidence: 61%

“…A function λ is subordinate to δ in U * and written as λ ðωÞ ≺ δðωÞ, if there exists a Schwarz function kðωÞ, which is holomorphic in U with kð0Þ = 0, such that λðωÞ = δðkðωÞÞ: Let ϕðωÞ be an analytic function with positive real part on U satisfies ϕð0Þ = 1 and ϕ ′ ð0Þ > 0 which maps U which is star shape with respect to ω = 1, also symmetric with respect to the real axis. We denote ∑ðϕÞ be the class of function λ∈∑ 1 for which −ωλ′ðωÞ/λðωÞ ≺ ϕðωÞ, ð ω ∈ U * Þ: The class ∑ðϕÞ was introduced and studied by Silverman et al [3] (see also [4]). The class ∑ðαÞ is a special case of the class ∑ðϕÞ when ϕðωÞ = 1 + ð1 − 2αÞω/1 − ω ð0 ≤ α < 1Þ:…”

Section: Introductionmentioning

confidence: 99%

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Application of Quasisubordination to Certain Classes of Meromorphic Functions

Shah

Hussain

Rasheed

et al. 2020

Journal of Function Spaces

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Inequalities play a fundamental role in many branches of mathematics and particularly in real analysis. By using inequalities, we can find extrema, point of inflection, and monotonic behavior of real functions. Subordination and quasisubordination are important tools used in complex analysis as an alternate of inequalities. In this article, we introduce and systematically study certain new classes of meromorphic functions using quasisubordination and Bessel function. We explore various inequalities related with the famous Fekete-Szego inequality. We also point out a number of important corollaries.

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“…Corollary 5. For φðωÞ = 1 and γ = 0 in Theorem 4, we obtain the result by Silverman et al [3] (see Theorem 4).…”

Section: Resultssupporting

confidence: 84%

Section: Corollary 6 Let λðωþsupporting

confidence: 81%

Section: Journal Of Function Spacesmentioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of Quasisubordination to Certain Classes of Meromorphic Functions

Shah

Hussain

Rasheed

et al. 2020

Journal of Function Spaces

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show abstract

“…Another interesting problem is to find the bound of Λ γ ( f ) := a 1 − γa 2 0 , γ ∈ C, which is known as Fekete-Szegö functional for meromorphic functions. Many authors examined the functional Λ γ ( f ) over subclasses of Σ (see [3][4][5]). The object of this paper is to investigate bounds of new functionals over the classes S * Σ (α), KΣ(α), SS * Σ (β) and SKΣ(β), generated by polynomials.…”

Section: Introductionmentioning

confidence: 99%

Bounds for the Coefficient of Faber Polynomial of Meromorphic Starlike and Convex Functions

et al. 2019

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Let Σ be the class of meromorphic functions f of the form f ( ζ ) = ζ + ∑ n = 0 ∞ a n ζ − n which are analytic in Δ : = { ζ ∈ C : | ζ | > 1 } . For n ∈ N 0 : = N ∪ { 0 } , the nth Faber polynomial Φ n ( w ) of f ∈ Σ is a monic polynomial of degree n that is generated by a function ζ f ′ ( ζ ) / ( f ( ζ ) − w ) . For given f ∈ Σ , by F n , i ( f ) , we denote the ith coefficient of Φ n ( w ) . For given 0 ≤ α < 1 and 0 < β ≤ 1 , let us consider domains H α and S β ⊂ C defined by H α = { w ∈ C : Re ( w ) > α } and S β = { w ∈ C : | arg ( w ) | < β } , which are symmetric with respect to the real axis. A function f ∈ Σ is called meromorphic starlike of order α if ζ f ′ ( ζ ) / f ( ζ ) ∈ H α for all ζ ∈ Δ . Another function f ∈ Σ is called meromorphic strongly starlike of order β if ζ f ′ ( ζ ) / f ( ζ ) ∈ S β for all ζ ∈ Δ . In this paper we investigate the sharp bounds of F n , n − i ( f ) , n ∈ N 0 , i ∈ { 2 , 3 , 4 } , for meromorphic starlike functions of order α and meromorphic strongly starlike of order β . Similar estimates for meromorphic convex functions of order α ( 0 ≤ α < 1 ) and meromorphic strongly convex of order β ( 0 < β ≤ 1 ) are also discussed.

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Some inequalities in relation with Fekete–Szegö problems specified by the Hadamard products of certain meromorphically analytic functions in the punctured unit disc

Zayed

Irmak

2019

Afr. Mat.

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Coefficient Bounds for Certain Classes of Meromorphic Functions

Cited by 13 publications

References 7 publications

Application of Quasisubordination to Certain Classes of Meromorphic Functions

Application of Quasisubordination to Certain Classes of Meromorphic Functions

Bounds for the Coefficient of Faber Polynomial of Meromorphic Starlike and Convex Functions

Some inequalities in relation with Fekete–Szegö problems specified by the Hadamard products of certain meromorphically analytic functions in the punctured unit disc

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