On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function

Serkan Çakmak; Sibel Yalcın

doi:10.36753/mathenot.1838201

On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function

Abstract

We introduce a new subclass $\Xi P_{H}^{0}(\lambda)$ of harmonic mappings in the unit disk defined via a differential inequality involving the convolution operator generated by the harmonic error function. We show that this inequality directly produces harmonic close-to-convex mappings of order $\lambda$, thereby establishing a structural connection between the harmonic error function and harmonic close-to-convex geometry. For this class, we derive sharp coefficient bounds, a sufficient coefficient condition, and growth and distortion estimates. Furthermore, we prove that $\Xi P_{H}^{0}(\lambda)$ is closed under convex combinations and harmonic convolution. Several examples are provided to illustrate the applicability of the obtained results. These findings place the harmonic error function within the framework of harmonic close-to-convex theory and provide a systematic operator-based approach to generating such mappings.

Keywords

Close-to-convexity, Convolution, Harmonic error function, Harmonic mappings

References

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Serkan Çakmak ^*
0000-0003-0368-7672
Türkiye

Sibel Yalcın
0000-0002-0243-8263
Türkiye

Early Pub Date

March 13, 2026

Publication Date

March 13, 2026

Submission Date

December 8, 2025

Acceptance Date

March 8, 2026

Published in Issue

Year 2026 Volume: 14 Number: 1

DOI

https://doi.org/10.36753/mathenot.1838201

IZ

https://izlik.org/JA53PP96NJ

APA

Çakmak, S., & Yalcın, S. (2026). On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function. Mathematical Sciences and Applications E-Notes, 14(1), 32-42. https://doi.org/10.36753/mathenot.1838201

AMA

1.Çakmak S, Yalcın S. On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function. Math. Sci. Appl. E-Notes. 2026;14(1):32-42. doi:10.36753/mathenot.1838201

Chicago

Çakmak, Serkan, and Sibel Yalcın. 2026. “On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function”. Mathematical Sciences and Applications E-Notes 14 (1): 32-42. https://doi.org/10.36753/mathenot.1838201.

EndNote

Çakmak S, Yalcın S (March 1, 2026) On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function. Mathematical Sciences and Applications E-Notes 14 1 32–42.

IEEE

[1]S. Çakmak and S. Yalcın, “On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function”, Math. Sci. Appl. E-Notes, vol. 14, no. 1, pp. 32–42, Mar. 2026, doi: 10.36753/mathenot.1838201.

ISNAD

Çakmak, Serkan - Yalcın, Sibel. “On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function”. Mathematical Sciences and Applications E-Notes 14/1 (March 1, 2026): 32-42. https://doi.org/10.36753/mathenot.1838201.

JAMA

1.Çakmak S, Yalcın S. On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function. Math. Sci. Appl. E-Notes. 2026;14:32–42.

MLA

Çakmak, Serkan, and Sibel Yalcın. “On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function”. Mathematical Sciences and Applications E-Notes, vol. 14, no. 1, Mar. 2026, pp. 32-42, doi:10.36753/mathenot.1838201.

Vancouver

1.Serkan Çakmak, Sibel Yalcın. On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function. Math. Sci. Appl. E-Notes. 2026 Mar. 1;14(1):32-4. doi:10.36753/mathenot.1838201