Bi-Bazilevič functions of order $ 
\vartheta +i\delta $ associated with $ (p, q)- $ Lucas polynomials

Ala Amourah; B. A. Frasin; G. Murugusundaramoorthy; Tariq Al-Hawary; Ala Amourah; B. A. Frasin; G. Murugusundaramoorthy; Tariq Al-Hawary

doi:10.3934/math.2021254

AIMS Mathematics

2021, Volume 6, Issue 5: 4296-4305. doi: 10.3934/math.2021254

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Research article

Bi-Bazilevič functions of order $ \vartheta +i\delta $ associated with $ (p, q)- $ Lucas polynomials

1.
Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid, Jordan
2.
Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq, Jordan
3.
Department of Mathematics, School of Advanced Sciences, VIT, Vellore 632014, Tamilnadu, India
4.
Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan

Received: 11 November 2020 Accepted: 20 January 2021 Published: 07 February 2021
MSC : 30C45

By means of$ (p, q)- $ Lucas polynomials, a class of Bazilevič functions of order $ \vartheta +i\delta $ in the open unit disk $ \mathbb{U} $ of analytic and bi-univalent functions is introduced. Further, we estimate coefficients bounds and Fekete-Szegö inequalities for functions belonging to this class. Several corollaries and consequences of the main results are also obtained.
- Bazilevič functions,
- Lucas polynomial,
- analytic functions,
- univalent functions,
- bi-univalent functions
Citation: Ala Amourah, B. A. Frasin, G. Murugusundaramoorthy, Tariq Al-Hawary. Bi-Bazilevič functions of order $ \vartheta +i\delta $ associated with $ (p, q)- $ Lucas polynomials[J]. AIMS Mathematics, 2021, 6(5): 4296-4305. doi: 10.3934/math.2021254

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Abstract

By means of$ (p, q)- $ Lucas polynomials, a class of Bazilevič functions of order $ \vartheta +i\delta $ in the open unit disk $ \mathbb{U} $ of analytic and bi-univalent functions is introduced. Further, we estimate coefficients bounds and Fekete-Szegö inequalities for functions belonging to this class. Several corollaries and consequences of the main results are also obtained.

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