A class of analytic functions related to convexity and functions with bounded turning

Zhi-Gang Wang; M. Naeem; S. Hussain; T. Mahmood; A. Rasheed; Zhi-Gang Wang; M. Naeem; S. Hussain; T. Mahmood; A. Rasheed

doi:10.3934/math.2020128

AIMS Mathematics

2020, Volume 5, Issue 3: 1926-1935. doi: 10.3934/math.2020128

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Research article

A class of analytic functions related to convexity and functions with bounded turning

1.
School of Mathematics and Computing Science, Hunan First Normal University, Changsha 410205, Hunan, P. R. China
2.
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
3.
Department of Mathematics, Comsats University Islamabad, Abbottabad Campus 22010, Pakistan

Received: 09 October 2019 Accepted: 14 February 2020 Published: 18 February 2020
MSC : 30C45, 30C80

In this paper, we define a new subclass $k$-$\mathcal{Q} (\alpha)$ of analytic functions, which generalizes the class of $k$-uniformly convex functions. Various interesting relationships between $k$-$\mathcal{Q} (\alpha)$ and the class $\mathcal{B}(\delta)$ of functions with bounded turning are derived.
- analytic functions,
- convex functions,
- uniformly convex functions,
- functions with bounded turning,
- subordination
Citation: Zhi-Gang Wang, M. Naeem, S. Hussain, T. Mahmood, A. Rasheed. A class of analytic functions related to convexity and functions with bounded turning[J]. AIMS Mathematics, 2020, 5(3): 1926-1935. doi: 10.3934/math.2020128

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Abstract

In this paper, we define a new subclass $k$-$\mathcal{Q} (\alpha)$ of analytic functions, which generalizes the class of $k$-uniformly convex functions. Various interesting relationships between $k$-$\mathcal{Q} (\alpha)$ and the class $\mathcal{B}(\delta)$ of functions with bounded turning are derived.

References

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