Some inequalities on Bazilevič class of functions involving quasi-subordination

K. R. Karthikeyan; G. Murugusundaramoorthy; N. E. Cho; K. R. Karthikeyan; G. Murugusundaramoorthy; N. E. Cho

doi:10.3934/math.2021417

AIMS Mathematics

2021, Volume 6, Issue 7: 7111-7124. doi: 10.3934/math.2021417

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Research article

Some inequalities on Bazilevič class of functions involving quasi-subordination

1.
Department of Applied Mathematics and Science, National University of Science & Technology (By Merger of Caledonian College of Engineering and Oman Medical College), Sultanate of Oman
2.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Deemed to be University, Vellore, Tamilnadu, India
3.
Department of Applied Mathematics, Pukyong National University, Busan 608-737, Korea

Received: 04 March 2021 Accepted: 19 April 2021 Published: 27 April 2021
MSC : 30C45

Quasi-subordination which is an extension of the majorization and subordination principle, has been used to define a subclass of Bazilevič functions of complex order. Various classes of analytic functions that map unit disc onto conic domains and some classes of special functions are studied in dual. Inequalities for the initial Taylor-Maclaurin coefficients and unified solution of Fekete-Szegö problem for subclasses of analytic functions related to various conic regions are our main results. Our main results have many applications which are presented in the form of corollaries.
- analytic functions,
- Bazilevič functions,
- starlike functions,
- subordination,
- Fekete-Szegö problem,
- coefficient inequalities,
- $ q $-calculus
Citation: K. R. Karthikeyan, G. Murugusundaramoorthy, N. E. Cho. Some inequalities on Bazilevič class of functions involving quasi-subordination[J]. AIMS Mathematics, 2021, 6(7): 7111-7124. doi: 10.3934/math.2021417

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Abstract

Quasi-subordination which is an extension of the majorization and subordination principle, has been used to define a subclass of Bazilevič functions of complex order. Various classes of analytic functions that map unit disc onto conic domains and some classes of special functions are studied in dual. Inequalities for the initial Taylor-Maclaurin coefficients and unified solution of Fekete-Szegö problem for subclasses of analytic functions related to various conic regions are our main results. Our main results have many applications which are presented in the form of corollaries.

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