Properties of $ \lambda $-pseudo-starlike functions with respect to a boundary point

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

doi:10.3934/math.2022486

AIMS Mathematics

2022, Volume 7, Issue 5: 8701-8714. doi: 10.3934/math.2022486

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Research article

Properties of $ \lambda $-pseudo-starlike functions with respect to a boundary point

1.
Department of Applied Mathematics, Pukyong National University, Busan 608-737, Korea
2.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, Tamilnadu, India
3.
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
4.
Department of Mathematics, University College of Engineering, Anna University, Tindivanam, India

Received: 17 January 2022 Revised: 22 February 2022 Accepted: 24 February 2022 Published: 02 March 2022
MSC : 30C45, 30C80

The purpose of this present paper is to investigate some mapping properties of functions which map the unit disc onto a overlapped leaf-like curve, having real part greater than zero. Also we define a class of $ \lambda $-pseudo starlike functions related to a leaf-like curve. Integral representation, inequalities for the initial Taylor-Maclaurin coefficients and Fekete-Szegö problem for subclasses of analytic functions related to various conic regions are obtained as our main results.
- analytic functions,
- starlike functions,
- functions with positive real part,
- subordination,
- Fekete-Szegö problem,
- coefficient inequalities,
- $ q $-calculus
Citation: N. E. Cho, G. Murugusundaramoorthy, K. R. Karthikeyan, S. Sivasubramanian. Properties of $ \lambda $-pseudo-starlike functions with respect to a boundary point[J]. AIMS Mathematics, 2022, 7(5): 8701-8714. doi: 10.3934/math.2022486

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Abstract

The purpose of this present paper is to investigate some mapping properties of functions which map the unit disc onto a overlapped leaf-like curve, having real part greater than zero. Also we define a class of $ \lambda $-pseudo starlike functions related to a leaf-like curve. Integral representation, inequalities for the initial Taylor-Maclaurin coefficients and Fekete-Szegö problem for subclasses of analytic functions related to various conic regions are obtained as our main results.

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