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Bounds on Initial Coefficients for a Certain New Subclass of Bi-univalent Functions by Means of Faber Polynomial Expansions

Bounds on Initial Coefficients for a Certain New Subclass of Bi-univalent Functions by Means of... In this paper, we present a new subclass $${\mathcal {T}}_{\varSigma }(\mu )$$ T Σ ( μ ) of bi univalent functions belong to $$\varSigma $$ Σ in the open unit disc $${\mathcal {U}} =\left\{ z\, :\,\,z\in {\mathcal {C}}\,\,and \,\, |z| <1\right\} $$ U = z : z ∈ C a n d | z | < 1 . Then, we use the concepts of Faber polynomial expansions to find upper bound for the general coefficient of such functions belongs to the defined class. Further, for the functions in this subclass we obtain bound on first three coefficients $$|a_{2}|$$ | a 2 | , $$|a_{3}|$$ | a 3 | and $$|a_{4}|$$ | a 4 | . We hope that this paper will inspire future researchers in applying our approach to other related problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics in Computer Science Springer Journals

Bounds on Initial Coefficients for a Certain New Subclass of Bi-univalent Functions by Means of Faber Polynomial Expansions

Mathematics in Computer Science , Volume 13 (3) – Jul 4, 2019

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References (27)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Nature Switzerland AG
Subject
Mathematics; Mathematics, general; Computer Science, general
ISSN
1661-8270
eISSN
1661-8289
DOI
10.1007/s11786-019-00406-7
Publisher site
See Article on Publisher Site

Abstract

In this paper, we present a new subclass $${\mathcal {T}}_{\varSigma }(\mu )$$ T Σ ( μ ) of bi univalent functions belong to $$\varSigma $$ Σ in the open unit disc $${\mathcal {U}} =\left\{ z\, :\,\,z\in {\mathcal {C}}\,\,and \,\, |z| <1\right\} $$ U = z : z ∈ C a n d | z | < 1 . Then, we use the concepts of Faber polynomial expansions to find upper bound for the general coefficient of such functions belongs to the defined class. Further, for the functions in this subclass we obtain bound on first three coefficients $$|a_{2}|$$ | a 2 | , $$|a_{3}|$$ | a 3 | and $$|a_{4}|$$ | a 4 | . We hope that this paper will inspire future researchers in applying our approach to other related problems.

Journal

Mathematics in Computer ScienceSpringer Journals

Published: Jul 4, 2019

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