Two Families of Bi-Univalent Functions Associating the (<i>p</i>, <i>q</i>)-Derivative with Generalized Bivariate Fibonacci Polynomials

Two Families of Bi-Univalent Functions Associating the (<i>p</i>, <i>q</i>)-Derivative with Generalized Bivariate Fibonacci Polynomials

Making use of generalized bivariate Fibonacci polynomials, we propose two families of regular functions of the type <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mrow><mo&...

Full description

Saved in:
Bibliographic Details
Main Authors: Sondekola Rudra Swamy, Basem Aref Frasin, Daniel Breaz, Luminita-Ioana Cotîrlă
Format: Article
Language:English
Published: MDPI AG 2024-12-01
Series:Mathematics
Subjects:
bi-univalent functions
(p, q)-derivative operator
subordination
Horodam polynomials
Fekete–Szegö functional
Online Access:https://www.mdpi.com/2227-7390/12/24/3933
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Making use of generalized bivariate Fibonacci polynomials, we propose two families of regular functions of the type <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mrow><mo>(</mo><mi>ζ</mi><mo>)</mo></mrow><mo>=</mo><mi>ζ</mi><mo>+</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>2</mn></mrow><mo>∞</mo></munderover></mstyle><msub><mi>d</mi><mi>j</mi></msub><msup><mi>ζ</mi><mi>j</mi></msup></mrow></semantics></math></inline-formula>, which are bi-univalent in the disc <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><mi>ζ</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi><mo>:</mo><mo>|</mo><mi>ζ</mi><mo>|</mo><mo><</mo><mn>1</mn><mo>}</mo></mrow></semantics></math></inline-formula> involving the (<i>p</i>, <i>q</i>)-derivative operator. We find estimates on the coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>d</mi><mn>2</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>d</mi><mn>3</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and the of Fekete–Szegö functional for members of these families. Relevant connections to the existing results and new consequences of the main result are presented.
ISSN:2227-7390

Similar Items