Surveys in Mathematics and its Applications
ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 21 (2026), 233 -- 256
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This work is licensed under a Creative Commons Attribution 4.0 International License.

HARMONIC FUNCTIONS WITH POSITIVE COEFFICIENTS INVOLVING TWO-PARAMETER MITTAG-LEFFLER TYPE POISSON DISTRIBUTION

K. Vijaya, K. Uma and G. Murugusundaramoorthy

Abstract. Making use of a special case of the two-parameter Mittag-Leffler type Poisson distribution, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and obtained the coefficient bounds. In addition to the distortion results and extreme points, there is a thorough discussion of inclusion relations, integral means, convolution properties, and partial sum results for this generalized class of functions.

2020 Mathematics Subject Classification: 30C45; 30C50
Keywords: Harmonic univalent functions; Harmonic functions with positive coefficients; Coefficient bounds; Integral means; Hadamard product; Partial sums; Two-parameter Mittag-Leffler function; Poisson distribution.

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Kaliappan Vijaya, ORCID: https://orcid.org/0000-0002-3216-7038
Department of Mathematics, School of Advanced Sciences
Vellore Institute of Technology(VIT), Vellore - 632014,   India
e-mail: kvijaya@vit.ac.in


Kaliappan Uma, ORCID: https://orcid.org/0000-0002-8030-9037
Department of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology(VIT), Vellore - 632014, India.
e-mail: kuma@vit.ac.in


Gangadharan Murugusundaramoorthy, ORCID: https://orcid.org/0000-0001-8285-6619
Department of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology(VIT), Vellore - 632014, India.
e-mail: gmsmoorthy@yahoo.com; gms@vit.ac.in




Received: February 10, 2026; Accepted: October 15, 2026
Published electronically: October 15, 2026