Some Properties and Graphical Applications of a New Subclass of Harmonic Functions Defined by a Differential Inequality

This paper establishes new results related to geometric function theory by presenting a new subclass of harmonic functions with complex values within the open unit disk, characterized by a second-order differential inequality. The investigation explores the bounds on the coefficients and estimates o...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-08, Vol.12 (15), p.2338
Main Authors: Yalçın, Sibel, Bayram, Hasan, Oros, Georgia Irina
Format: Article
Language:English
Subjects:
Applied mathematics
coefficient estimates
convolution
graphics
harmonic function
Harmonic functions
Inequality
Investigations
Partial differential equations
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Summary:This paper establishes new results related to geometric function theory by presenting a new subclass of harmonic functions with complex values within the open unit disk, characterized by a second-order differential inequality. The investigation explores the bounds on the coefficients and estimates of the function growth. This paper also demonstrates that this subclass remains stable under the convolution operation applied to its members. In addition, in the last section, images of the unit disk under some functions of this class are given.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12152338