On Convex Functions with Complex Order Through Bounded Boundary Rotation

S. Melike Aydoğan; F. Müge Sakar

doi:10.1007/s11786-019-00405-8

On Convex Functions with Complex Order Through Bounded Boundary Rotation

S. Melike Aydoğan^*, F. Müge Sakar

^*Corresponding author for this work

Department of Mathematics Engineering

Batman University

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let F be the class of functions f(z) = z+ a₂z²+ ⋯ which are analytic in D= { z: | z| < 1 } and satisfies the condition 1+1bzf′′(z)f′(z)=pt(z),(b≠0,b∈C,z∈D)where pt(z)=(t4+12)p1(z)-(t4-12)p2(z), t≥ 2 , p₁(z) , p₂(z) ∈ P. P is the class of analytic functions with the positive real part (Caratheodory class) then this function will be called convex function by means of bounded boundary rotation and denoted by K(t, b). In this present paper, we will introduce this class and its some properties.

Original language	English
Pages (from-to)	433-439
Number of pages	7
Journal	Mathematics in Computer Science
Volume	13
Issue number	3
DOIs	https://doi.org/10.1007/s11786-019-00405-8
Publication status	Published - 1 Sept 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Funding

The work presented here by first-named author is supported by Istanbul Technical University Scientific Research Project Coordination Unit. Project Number: TGA-2018-41339. The work presented here by first-named author is supported by Istanbul Technical University Scientific Research Project Coordination Unit. Project Number: TGA-2018-41339.

Funders	Funder number
Istanbul Technical University Scientific Research Project Coordination Unit
Istanbul Teknik Üniversitesi	TGA-2018-41339

Keywords

Analytic function
Coefficient estimates
Convex function
Radius of starlikeness

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10.1007/s11786-019-00405-8

Cite this

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abstract = "Let F be the class of functions f(z) = z+ a2z2+ ⋯ which are analytic in D= { z: | z| < 1 } and satisfies the condition 1+1bzf′′(z)f′(z)=pt(z),(b≠0,b∈C,z∈D)where pt(z)=(t4+12)p1(z)-(t4-12)p2(z), t≥ 2 , p1(z) , p2(z) ∈ P. P is the class of analytic functions with the positive real part (Caratheodory class) then this function will be called convex function by means of bounded boundary rotation and denoted by K(t, b). In this present paper, we will introduce this class and its some properties.",

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AB - Let F be the class of functions f(z) = z+ a2z2+ ⋯ which are analytic in D= { z: | z| < 1 } and satisfies the condition 1+1bzf′′(z)f′(z)=pt(z),(b≠0,b∈C,z∈D)where pt(z)=(t4+12)p1(z)-(t4-12)p2(z), t≥ 2 , p1(z) , p2(z) ∈ P. P is the class of analytic functions with the positive real part (Caratheodory class) then this function will be called convex function by means of bounded boundary rotation and denoted by K(t, b). In this present paper, we will introduce this class and its some properties.

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KW - Coefficient estimates

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On Convex Functions with Complex Order Through Bounded Boundary Rotation

Abstract

Bibliographical note

Funding

Keywords

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