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On A Subclass of Harmonic Univalent Funtions Associated with the Differential Operator

B Ravindar, R. B. Sharma · 2018 📄 find paper →

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Abstract

In this paper, a new subclass of harmonic univalent functions in the unit disk   : 1 U z C z =   is introduced using a differential operator. Also the coefficient estimates, convolution conditions, extreme points and convex combinations are obtained.

Results & Lemmas (3)

Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.

Theorem 2.1 Theorem 2.1: Let f h g = + be given by (1.1). If 2 1 [( 1)( ) ] [( ) (1 )((
Theorem 2.1: Let f h g = + be given by (1.1). If 2 1 [( 1)( ) ] [( ) (1 )((
Theorem 2.2 Theorem 2.2: Let n n f h g = + be given by (1.4). Then (,,,,, ) H
Theorem 2.2: Let n n f h g = + be given by (1.4). Then ( , , , , , ) H
Theorem 3.1 Theorem 3.1: For 0,n N , 0 ,,, 0, 0 w w  
Theorem 3.1: For 0 ,n N  , 0  , , , 0, 0 w w  

Definitions (1)

Def 1.1 Definition 1.1: We define a new subclass (,,,,, ) H B n w 
Definition 1.1: We define a new subclass ( , , , , , ) H B n w 
Function classes studied:
bi-univalent

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