Multivalent harmonic functions involving multiplier transformation

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

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