On certain classes of bi-univalent functions related to \(m\)-fold symmetry

Volume 11, Issue 4, pp 490--499 http://dx.doi.org/10.22436/jnsa.011.04.06

Publication Date: March 17, 2018 Submission Date: September 19, 2017 Revision Date: December 01, 2017 Accteptance Date: December 06, 2017

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Authors

Saqib Hussain - COMSATS Institute of Information Technology, Abbotabad, Pakistan. Shahid Khan - Department of Mathematics, Riphah International University Islamabad, Pakistan. Muhammad Asad Zaighum - Department of Mathematics, Riphah International University Islamabad, Pakistan. Maslina Darus - School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia 43600, Bangi, Selangor, Malaysia.

Abstract

In our present investigation, we introduce two new subclasses \(S_{\Sigma _{m}}(\alpha ,\lambda ,\mu )\) and \(S_{\Sigma _{m}}(\beta ,\lambda ,\mu )\) of analytic and \(m\)-fold symmetric bi-univalent functions in the open unit disk \(E\). Results concerning coefficient estimates for the functions of these classes are derived. Many interesting new and already existing corollaries are also presented.

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Keywords

• \(m\)-Fold symmetry
• bi-univalent functions
• coefficient estimates

MSC

•  30C45
•  30C50

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