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Research Articles

Radii problems and some other properties of certain classes of analytic functions with boundary rotation

Authors:

A. Saliu ,

COMSATS University Islamabad, PK
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K.I. Noor

COMSATS University, PK
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Abstract

In this work, we introduce some generalized classes of convex, close-to-convex, quasi-convex and strongly convex functions f(z) in the frame of a unit disc U. Our first task is to discuss some geometric properties of a class of functions f(z) for which f(U) has a boundary rotation of at most mπ, m ≥ 2. Furthermore, we determine the smallest disc of the linear combinations of functions belonging to the classes Vm [A, B], CCVm1m2 [A, B, C, D] and QCVm1m2 [A, B, C, D]. Condition for univalence, covering theorem and distortion result of a more generalized strongly close-to-convex functions are also obtained. Remarkable cases and the consequences of the investigation are also highlighted in the paper.

How to Cite: Saliu, A. and Noor, K.I., 2021. Radii problems and some other properties of certain classes of analytic functions with boundary rotation. Journal of the National Science Foundation of Sri Lanka, 49(3), pp.429–439.
Published on 30 Nov 2021.
Peer Reviewed

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