Certain Properties of Harmonic Functions Defined by a Second-Order Differential Inequality

Article Mathematics

Some Properties of Certain Multivalent Harmonic Functions

Georgia Irina Oros et al.

Summary: This paper analyzes various features of a new class of normalized multivalent harmonic functions, including coefficients bounds, growth estimations, starlikeness, and convexity radii. It further demonstrates the closure property of this class under convolution operation. Moreover, it shows that several previously introduced and investigated classes of multivalent harmonic functions are special cases of this class.

MATHEMATICS (2023)

Add to Collection

Article Multidisciplinary Sciences

q-Analogue of a New Subclass of Harmonic Univalent Functions Associated with Subordination

Hasan Bayram

Summary: This article introduces and investigates the q-analogue of a new subclass of harmonic univalent functions defined by subordination. Coefficient characterization, compactness and extreme points, distortion bounds, and necessary and sufficient convolution conditions for this subclass with negative coefficients are obtained. The symmetry properties and other properties of the q-analogue subclass of functions presented in this paper shed light on future studies.

SYMMETRY-BASEL (2022)

Add to Collection

Article Mathematics

Some basic geometric properties of a subclass of harmonic mappings

Serkan Cakmak et al.

Summary: In this paper, a new subclass of complex-valued harmonic functions in the open unit disk is introduced and various properties such as coefficient bounds, growth estimates, radius of univalency, radius of starlikeness, and radius of convexity are investigated. Additionally, it is shown that this class is closed under convolution of its members.

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA (2022)

Add to Collection

Article Mathematics

On a subclass of close-to-convex harmonic mappings

Rajbala et al.

Summary: This paper introduces a new class of sense-preserving harmonic mappings in the open unit disk and proves that functions in this class are close-to-convex. Basic properties such as coefficient bounds, growth estimates, and convolution are discussed, along with the determination of the radius of convexity for functions in this family. Additionally, certain harmonic univalent polynomials belonging to this family are constructed.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS (2021)

Add to Collection

Article Mathematics

Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality

Elif Yasar et al.

Summary: In this paper, a class of normalized harmonic functions in the unit disk satisfying a third-order differential inequality is considered, and various properties of this class are investigated. Harmonic polynomials involving Gaussian hypergeometric function belonging to this class are constructed as an application, with graphical examples provided using Maple software.

TURKISH JOURNAL OF MATHEMATICS (2021)

Add to Collection

Article Mathematics