Geometric Properties of Harmonic Function Affiliated With Fractional Operator

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DOI: https://doi.org/10.28924/2291-8639-22-2024-133
Published: Aug 12, 2024
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Kuppuraj Divya Priya, K. Thilagavathi, Geometric Properties of Harmonic Function Affiliated With Fractional Operator, Int. J. Anal. Appl., 22 (2024), 133.

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Kuppuraj Divya Priya, K. Thilagavathi

Abstract

This paper's goal is to discover new results for the harmonic univalent functions G=υ+η defined in the open unit disc ρ={z: |z|<1}. Examining KS indicates the set of all analytic harmonic functions of form G in the open unit disc ρ. The convolution featuring the Mittag-Leffler function and fractional operator is applied to generate the family of harmonic univalent VKS. Motivated by Kamali [9], we present a novel of kamali class with VKS(δ) brand-new class of harmonic univalent functions Pα,β,zγ,δ,ε,ν inspiring inequality. Analysing Mittag-Leffler function convolution with modified tremblay operator inequality as a necessary and sufficient condition for univalent harmonic functions related to specific generalised Mittag-Leffler functions to be in the function class VKS(δ) is the aim of this research. Moreover, we discover extreme points, a distortion theorem, convolution properties, and convex combinations for the functions in VKS(δ).

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