Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

• Main Authors: Hari Mohan Srivastava, Ahmad Motamednezhad, Safa Salehian
• Format: Article
• Language: English
• Published: MDPI AG 2021-02-01
• Series: Axioms
• Subjects: analytic functions; univalent and bi-univalent functions; meromorphic bi-univalent functions; coefficient estimates; Faber polynomial expansion; meromorphic bi-Bazilevič functions of order β and type μ
• Online Access: https://www.mdpi.com/2075-1680/10/1/27

In this paper, we introduce a new comprehensive subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Σ</mi><mi>B</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of meromorphic bi-univalent functions in the open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">U</mi></semantics></math></inline-formula>. We also find the upper bounds for the initial Taylor-Maclaurin coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>b</mi><mn>0</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>b</mi><mn>1</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>b</mi><mn>2</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>b</mi><mi>n</mi></msub><mrow><mo>|</mo><mspace width="0.277778em"></mspace><mrow><mo>(</mo><mi>n</mi><mo>≧</mo><mn>1</mn><mo>)</mo></mrow></mrow></mrow></semantics></math></inline-formula> for functions in the subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Σ</mi><mi>B</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.