On the Starlikeness of Certain Class of Multivalent Analytic Functions

Shi, Lei; Wang, Zhi-Gang

doi:10.1155/2014/738350

Search citation statements

Order By: Relevance

Paper Sections

Select...

Bounds For Auxiliary Linear Operators Acting On B P (α β λ; J)1

Criteria For P-valent Starlike Functions In B P (α β λ; J)1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This completes the proof of Theorem 3.1. 2 Remark 3.2 If α = β = 1 in Theorem 3.1, we obtain a result found in [10,Lemma 5].…”

Section: Bounds For Auxiliary Linear Operators Acting On B P (α β λ; J)supporting

confidence: 73%

See 1 more Smart Citation

Some properties for a class of analytic functions defined by a higher-order differential inequality

Al-Refai¹

2019

Turk J Math

View full text Add to dashboard Cite

Let Bp(α, β, λ; j) be the class consisting of functions f (z) = z p + ∑ ∞ k=p+1 a k z k , p ∈ N which satisfy Re { α f (j) (z) z p−j + β f (j+1) (z) z p−j−1 + (β − α 2) f (j+2) (z) z p−j−2 } > λ, (z ∈ U = {z : |z| < 1}), for some λ (λ < p!{α+(p−j)β +(p−j)(p−j −1)(β −α)/2}/(p−j)!) and j = 0, 1, ..., p , where p+1−j +2α/(β −α) > 0 or α = β = 1. The extreme points of Bp(α, β, λ; j) are determined and various sharp inequalities related to Bp(α, β, λ; j) are obtained. These include univalence criteria, coefficient bounds, growth and distortion estimates and bounds for certain linear operators. Furthermore, inclusion properties are investigated and estimates on λ are found so that functions of Bp(α, β, λ; j) are p-valent starlike in U. For instance, Re{zf ′′ (z)} > (5 − 12 ln 2)/(44 − 48 ln 2) ≈ −0.309 is sufficient condition for any normalized analytic function f to be starlike in U. The results improve and include a number of known results as their special cases.

show abstract

“…This completes the proof of Theorem 3.1. 2 Remark 3.2 If α = β = 1 in Theorem 3.1, we obtain a result found in [10,Lemma 5].…”

Section: Bounds For Auxiliary Linear Operators Acting On B P (α β λ; J)supporting

confidence: 73%

“…This result was obtained by many authors, see [10,12]. By the aid of the Alexander's relation (f (z) ∈ CV ⇐⇒ zf ′ (z) ∈ S * ) , we have the following consequence result from Theorem 5.5 and Lemma 1.1.…”

Section: Criteria For P-valent Starlike Functions In B P (α β λ; J)supporting

confidence: 54%

Some properties for a class of analytic functions defined by a higher-order differential inequality

Al-Refai¹

2019

Turk J Math

View full text Add to dashboard Cite

show abstract

On the Starlikeness of Certain Class of Multivalent Analytic Functions

Cited by 1 publication

References 24 publications

Some properties for a class of analytic functions defined by a higher-order differential inequality

Some properties for a class of analytic functions defined by a higher-order differential inequality

Contact Info

Product

Resources

About