<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we introduce a new subclass of analytic functions with negative coefficients defined by Gegenbauer polynomials. We obtain coefficient bounds, growth and distortion properties, extreme points and radii of starlikeness, convexity and close-to-convexity for functions belonging to the class <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/tmmp-2021-0006_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mi>T</mi><msubsup><mi>S</mi><mi>λ</mi><mi>m</mi></msubsup><mo stretchy="false">(</mo><mi>γ</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>v</mi><mo stretchy="false">)</mo></mrow></math><tex-math>TS_\lambda ^m(\gamma ,e,k,v)</tex-math></alternatives></inline-formula>. Furthermore, we obtained the Fekete-Szego problem for this class.</p>
</abstract>

In this paper, we introduce a new subclass of analytic functions with negative coefficients defined by Gegenbauer polynomials. We obtain coefficient bounds, growth and distortion properties, extreme points and radii of starlikeness, convexity and close-to-convexity for functions belonging to the class TSλm(γ,e,k,v)TS_\lambda ^m(\gamma ,e,k,v). Furthermore, we obtained the Fekete-Szego problem for this class.

A Certain Subclass of Analytic Functions with Negative Coefficients Defined by Gegenbauer Polynomials

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we introduce a new subclass of analytic functions with negative coefficients defined by Gegenbauer polynomials. We obtain coefficient bounds,...

A Certain Subclass of Analytic Functions with Negative Coefficients Defined by Gegenbauer Polynomials

Published Online: Jan 01, 2022

Page range: 73 - 84

Received: Nov 11, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0006

Keywords
analytic, coefficient bounds, extreme points, convolution, polynomial

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Certain Subclass of Analytic Functions with Negative Coefficients Defined by Gegenbauer Polynomials

Published Online: Jan 01, 2022

Page range: 73 - 84

Received: Nov 11, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0006

Keywordsanalytic, coefficient bounds, extreme points, convolution, polynomial

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
analytic, coefficient bounds, extreme points, convolution, polynomial