Convolution features of univalent meromorphic functions generated by Barnes-Mittag-Leffler function

Tuğba Yavuz; Şahsene Altınkaya

doi:10.2478/auom-2026-0014

.blurhash-client-img { display: none !important; }

Convolution features of univalent meromorphic functions generated by Barnes-Mittag-Leffler function

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 34 (2026): Issue 1 (May 2026)

By: Tuğba Yavuz and Şahsene Altınkaya

Open Access

|May 2026

Abstract

The Mittag-Leffler function plays an important role in Geometric Function Theory, particularly in the study of analytic and meromorphic function classes. Among its various generalizations, the Barnes-Mittag-Leffler function stands out due to its intricate structure and applications in diverse mathematical fields. In this paper, our main focus is to investigate the convolution properties of these functions and establish conditions that ensure specific geometric characteristics. Additionally, we explore membership relations for functions in these classes. The results obtained in this work are novel, and their significance is demonstrated through various illustrative consequences and corollaries, emphasizing their potential impact in function theory and its applications.

References

A. A. Abubaker, K. Matarneh, S. B. Al-Shaikh, M. F. Khan, Some new applications of the fractional integral and four-parameter Mittag-Leffler function, PloS One. 20 (2) (2025), 1–18.
Search in Google Scholar Back to article
A. Alenazi, K. Mehrez, Further geometric properties of the Barnes-Mittag-Leffler function, Axioms. 13 (1) (2023), 1–14.
Search in Google Scholar Back to article
Ş. Altınkaya, On the inclusion properties for ϑ-spirallike functions involving both Mittag-Leffler and Wright function, Turkish Journal of Mathematics. 46 (3) (2022), 1119–1131.
Search in Google Scholar Back to article
Ş. Altınkaya, Some properties for spirallike functions by means of both Mittag-Leffler and Wright function, Comptes Rendus de lAcadmie Bulgare des Sciences. 74 (10) (2021), 1431–1441.
Search in Google Scholar Back to article
D. Bansal, K. Mehrez, On a new class of functions related with Mittag-Leffler and Wright functions and their properties, Communications of the Korean Mathematical Society. 35 (4) (2020), 1123–1132.
Search in Google Scholar Back to article
D. Bansal, J. K. Prajapat, Certain geometric properties of the Mittag-Leffler functions, Complex Variables and Elliptic Equations. 61 (3) (2016), 338–350.
Search in Google Scholar Back to article
E. W. Barnes, The asymptotic expansion of integral functions defined by Taylor’s series, Philosophical Transactions of the Royal Society of London. Series A. 206 (402–412) (1906), 249–297.
Search in Google Scholar Back to article
T. Bulboaca, M. K. Aouf, R. M. El-Ashwah, Convolution properties for subclasses of meromorphic univalent functions of complex order, Filomat. 26 (1) (2012), 153–163.
Search in Google Scholar Back to article
D. Breaz, K. R. Karthikeyan, G. Murugusundaramoorthy, Applications of MittagLeffler functions on a subclass of meromorphic functions influenced by the definition of a non-Newtonian derivative, Fractal and Fractional. 8 (9) (2024), 1–9.
Search in Google Scholar Back to article
G. A. Dorrego, R. A. Cerutti, The k-Mittag-Leffler function, International Journal of Contemporary Mathematical Sciences. 7 (13–16) (2012), 705–716.
Search in Google Scholar Back to article
P. L. Duren, Univalent functions, Springer Science & Business Media, 2001.
Search in Google Scholar Back to article
M. Garg, P. Manohar, S. L. Kalla, A Mittag-Leffler-type function of two variables, Integral Transforms and Special Functions. 24 (2013), 934–944.
Search in Google Scholar Back to article
K. S. Gehlot, The p − k Mittag-Leffler function, Palestine Journal of Mathematics. 7 (2) (2018), 628–632.
Search in Google Scholar Back to article
R. Gorenflo, A. A. Kilbas, F. Mainardi, S. V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications, 2nd ed., Springer, New York, 2020.
Search in Google Scholar Back to article
M. Haji Mohd, R. M. Ali, L. S. Keong, V. Ravichandran, Subclasses of meromorphic functions associated with convolution, Journal of Inequalities and Applications. 2009 (1) (2009), 1–9.
Search in Google Scholar Back to article
P. Humbert, Quelques resultants retifs a la fonction de Mittag-Leffler, Comptes Rendus Hebdomadaires des Seances de lAcademie des Sciences. 236 (1953), 1467–1468.
Search in Google Scholar Back to article
P. Humbert, R. P. Agarwal, Sur la fonction de Mittag-Leffler et quelques unes de ses generalizations, Bulletin des Sciences Mathmatiques. 77 (1953), 180–185.
Search in Google Scholar Back to article
M. Kamarujjama, N. U. Khan, O. Khan, J. J. Nieto, Extended type k-Mittag-Leffler function and its applications, International Journal of Applied and Computational Mathematics. 5 (3) (2019), 1–14.
Search in Google Scholar Back to article
Yu. Luchko, The Wright function and its applications, in A. Kochubei, Yu. Luchko (Eds.), Handbook of Fractional Calculus with Applications Volume 1: Basic Theory, De Gruyter, Berlin/Boston, 2019, pp. 241–268.
Search in Google Scholar Back to article
K. Mehrez, S. Das, A. Kumar, Monotonicity properties and functional inequalities for the Barnes-Mittag-Leffler function, Miskolc Mathematical Notes. 24 (2023), 893–907.
Search in Google Scholar Back to article
G. M. Mittag-Leffler, Sur la nouvelle fonction E_α (x), C. R. Acad. Sci. Paris. 137 (1903), 554–558.
Search in Google Scholar Back to article
A. O. Mostafa, M. K. Aouf, H. M. Zayed, T. Bulboacă, Convolution conditions for subclasses of meromorphic functions of complex order associated with basic Bessel functions, Journal of the Egyptian Mathematical Society. 25 (3) (2017), 286–290.
Search in Google Scholar Back to article
A. R. I. F. Muhammad, J. Sokol, A. Y. A. Z. Muhammad, Sufficient condition for functions to be in a class of meromorphic multivalent Sakaguchi type spiral-like functions, Acta Mathematica Scientia. 34 (2) (2014), 575–578.
Search in Google Scholar Back to article
S. Ponnusamy, Convolution properties of some classes of meromorphic univalent functions, Proceedings of the Indian Academy of Sciences -Mathematical Sciences. 103 (1993), 73–89.
Search in Google Scholar Back to article
V. Ravichandran, S. S. Kumar, K. G. Subramanian, Convolution conditions for spirallikeness and convex spirallikeness of certain meromorphic p-valent functions, Journal of Inequalities in Pure and Applied Mathematics. 5 (1) (2004), 1–7.
Search in Google Scholar Back to article
L. Shi, Z. G. Wang, On certain subclass of meromorphic spirallike functions involving the hypergeometric function, The Scientific World Journal. 2014 (1) (2014), 1–7.
Search in Google Scholar Back to article
L. Shi, Z. G. Wang, M. H. Zeng, Some subclasses of multivalent spirallike meromorphic functions, Journal of Inequalities and Applications. 2013 (1) (2013), 1–12.
Search in Google Scholar Back to article
A. K. Shukla, J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties, Journal of Mathematical Analysis and Applications. 336 (2007), 797–811.
Search in Google Scholar Back to article
B. Stankovic, L. Gajic, Some properties of Wright’s function, Publications de l’Institut Mathmatique. 34 (1976), 91–98.
Search in Google Scholar Back to article
A. Wiman, ber den Fundamentalsatz in der Theorie der Functionen E_α (x), Acta Mathematica. 29 (1905), 191–201.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2026-0014 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 279 - 293

Submitted on: May 8, 2025

Accepted on: Oct 9, 2025

Published on: May 15, 2026

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Barnes-Mittag-Leffler function,

Meromorphic spirallike functions,

Related subjects:

© 2026 Tuğba Yavuz, Şahsene Altınkaya, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 34 (2026): Issue 1 (May 2026)