$ q $-Noor integral operator associated with starlike functions and $ q $-conic domains

Syed Ghoos Ali Shah; Shahbaz Khan; Saqib Hussain; Maslina Darus; Syed Ghoos Ali Shah; Shahbaz Khan; Saqib Hussain; Maslina Darus

doi:10.3934/math.2022606

AIMS Mathematics

2022, Volume 7, Issue 6: 10842-10859. doi: 10.3934/math.2022606

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$ q $-Noor integral operator associated with starlike functions and $ q $-conic domains

1.
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan
2.
Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia

Received: 14 January 2022 Revised: 10 March 2022 Accepted: 14 March 2022 Published: 31 March 2022
MSC : Primary 30C45, Secondary 30C50

In this paper, we will discuss some generalized classes of analytic functions related with conic domains in the context of $ q $-calculus. In this work, we define and explore Janowski type $ q $-starlike functions in $ q $ -conic domains. We investigate some important properties such as necessary and sufficient conditions, coefficient estimates, convolution results, linear combination, weighted mean, arithmetic mean, radii of starlikeness, growth and distortion results for these classes. It is important to mention that our results are generalization of number of existing results.
- analytic functions,
- subordination,
- Noor integral operator,
- $ q $-conic domain,
- $ q $-Janowski functions
Citation: Syed Ghoos Ali Shah, Shahbaz Khan, Saqib Hussain, Maslina Darus. $ q $-Noor integral operator associated with starlike functions and $ q $-conic domains[J]. AIMS Mathematics, 2022, 7(6): 10842-10859. doi: 10.3934/math.2022606

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Abstract

In this paper, we will discuss some generalized classes of analytic functions related with conic domains in the context of $ q $-calculus. In this work, we define and explore Janowski type $ q $-starlike functions in $ q $ -conic domains. We investigate some important properties such as necessary and sufficient conditions, coefficient estimates, convolution results, linear combination, weighted mean, arithmetic mean, radii of starlikeness, growth and distortion results for these classes. It is important to mention that our results are generalization of number of existing results.

References

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