Surveys in Mathematics and its Applications
ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 21 (2026), 257 -- 274
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This work is licensed under a Creative Commons Attribution 4.0 International License.

A CLASS OF ANALYTIC FUNCTIONS ASSOCIATED WITH A MITTAG-LEFFLER-TYPE POISSON DISTRIBUTION

P. Thirupathi Reddy

Abstract. In this paper, we introduce and investigate a new subclass of analytic functions with negative coefficients associated with a Poisson distribution generated by a special case of the classical two-parameter Mittag--Leffler function. A convolution operator corresponding to the associated Poisson distribution series is first defined and employed to construct the desired function class. For this newly introduced class, we establish coefficient estimates, necessary and sufficient conditions, distortion inequalities, extreme point representations, closure properties, convolution and integral transform results, neighbourhood properties, integral mean inequalities, and various radius problems. The results obtained in this work extend several known investigations concerning probability distribution operators in geometric function theory and demonstrate further applications of Mittag--Leffler-type Poisson distribution series in the study of analytic functions.

2020 Mathematics Subject Classification: 30C45, 30C50.
Keywords: Analytic functions; Univalent functions; Mittag--Leffler function; Poisson distribution; Hadamard product; Coefficient estimates; Subordination; Integral transform.

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P. Thirupathi Reddy, ORCID: https://orcid.org/0009-0000-9846-9883
Department of Mathematics, D.R.K. Institute of Science and Technology,
Bowrampet, Hyderabad--500043, Telangana, India.
e-mail: reddypt2@gmail.com


Received: May 11, 2026; Accepted: October 16, 2026
Published electronically: October 17, 2026