Multivalent harmonic functions involving multiplier transformation

Year 2022, Volume: 71 Issue: 3, 731 - 751, 30.09.2022

Vimlesh Gupta , Saurabh Porwal , Omendra Mishra

https://doi.org/10.31801/cfsuasmas.962040

Abstract

In the present investigation we study a subclass of multivalent harmonic functions involving multiplier transformation. An equivalent convolution class condition and a sufficient coefficient condition for this class is acquired. We also show that this coefficient condition is necessary for functions belonging to its subclass. As an application of coefficient condition, a necessary and sufficient hypergeometric inequality is also given. Further, results on bounds, inclusion relation, extreme points, a convolution property and a result based on the integral operator are obtained.

Keywords

Multivalent harmonic functions, uniformly starlike functions, generalized hypergeometric functions, convolution

Supporting Institution

None

Project Number

NA

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