A Study on Analytic Functions Associated with the Generalized Hurwitz-Lerch zeta Function

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Published: Sep 10, 2025
DOI: https://doi.org/10.26629/uzjns.2025.09

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afaf A abubaker
University of Zawia
https://orcid.org/0009-0008-5713-5308

Abstract

In this study, we introduce and investigate new subclasses of analytic functions that are closely related to the generalized Hurwitz-Lerch zeta function. We establish certain inclusion relationships among these classes, and also consider the application of an associated integral operator within this context.

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How to Cite
[1]
afaf A. abubaker, “A Study on Analytic Functions Associated with the Generalized Hurwitz-Lerch zeta Function”, UZJNS, vol. 2, no. 2, pp. 71–76, month-09 2025.
Issue
Vol. 2 No. 2 (2025): Univ Zawia J Nat Sci
Section
Mathematics
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

References

Bieberbach, Ludwig, “U ̈ber die koeffizienten derjenigen potenzreihen, welche eine schlichte

abbildung des einheitskreises vermitteln,” Preuss. Akad. Wiss.Sitzungsb,138,1916, pp. 940–955.

De Branges, Louis, “A proof of the Bieberbach conjecture,” Acta Math. 154, 1985, pp. 137–152.

Abubaker, Afaf, “On some classes of analytic functions by involving n-th Hadamard product,” Journal of Faculties of Education, 2020, pp.1-13.

Lin, Shy-Der, and H. M. Srivastava, “Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations,” Appl. Math. Comput., 154,2004 pp. 725-733.

Choi, Junesang, and Rakesh K. Parmar, “An extension of the generalizedHurwitz-Lerch Zeta function of two variables,” Filomat ,3,2017,91-96.

Srivastava, Hari M,“Generating relations and other results associated with some families of the extended Hurwitz-Lerch Zeta functions, ”

SpringerPlus,2013.

Khan, Waseem A., M. Ghayasuddin, and Moin Ahmad, “Certian new extension of Hurwitz-Lerch Zeta function,” J.Math. and Informatics,37,2019, pp.13-21.

Nadeem, Raghib, et al. “Analytical properties of the Hurwitz–Lerch zeta function”, Advances in Difference Equations 2020,1, 466.

Hadi, Sarem H., and Maslina Darus, “(p,q)-Chebyshev polynomials for the families of biunivalent function associating a new integral operator with(p,q)-Hurwitz zeta function function,”Turk.J.Math., 46,2022, pp.2415-2429.

Cho, Nak Eun, Oh Sang Kwon, and Hari M. Srivastava, “Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators,” J. Math. Anal. Appl., 292 ,2004, pp.470-483.

Carlson, B. C., and Dorothy B. Shaffer, “Starlike and prestarlike hypergeometric functions,” SIAM J. Math. Anal. 15 ,1984, pp. 737-745.

Noor, K. Inayat, “On new classes of integral operators,” J. Natur. Geom., 16,1999, pp. 71-80.

Uralegaddi, B. A., and C. Somanatha, “Certain classes of univalent functions,” In. H.M. Srivastava and S. Owa (eds.). Current Topics in Analytic Function Theory,1992, pp. 371-374.

Jung, Il Bong, Young Chan Kim, and H. M. Srivastava, “The Hardy space of analytic functions associated with certain one parameter families of integral operators,”J. Math.,Anal. Appl. 176,1, 1993, pp. 138-147.

KomatuY , .“On analytical prolongation of a family of operators, ”Math. (cluj), 32 ,55,1990, pp. 141-145.

Cho, Nak Eun, Oh Sang Kwon, and H. M. Srivastava, “Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations,”J. Math. Anal. Appl. 300,2004, pp. 505-520.

Salagean, Grigore Stefan, “Subclasses of univalent functions,” Complex Analysis-Fifth Romanian-Finnish Seminar: Part 1 Proceedings of the Seminar held in Bucharest, June 28–July 3, 1981. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006.

Ruscheweyh, Stephan, “New criteria for univalent functions,” Proc. Amer. Math.Soc,49, 1975, pp.109-115.

Govindaraj,M. and SrikandanSivasubramanian , “On a Class of Analytic Functions Related to Conic Domains Involving q- Calculus,” Analysis Mathematica,43 ,2017, 475-487.

Robertson, Malcolm IS, “On the theory of univalent functions,” Ann. Math.,1936, pp.374-408.

Libera, Richard J., “Some radius of convexity problems,”, 1964, 143-158.

Noor, Khalida Inayat, “On quasi-convex functions and related topics,” Internat. J.Math. Math. Sci., 10, 1987, pp. 241-258.

Bernardi S. D., “Convex and starlike univalent functions,”Trans. Amer.Math. Soc., 135 ,1969, pp. 429-446.

Libera, Richard J., “Some classes of regular univalent functions,”Proc. Amer.Math. Soc., 16 ,1965, 755-658.

Livingston A. E., “On the radius of univalence of certain analytic functions,”Proc. Amer. Math. Soc., 17 ,1966, pp.352-357.

Miller, Sanford, “Differential inequalities and Carathodory function,” Bull.Amer. Math. Soc., 1975, pp. 79-81.

Jack I. S, “Functions starlike and convex of order α,” J. London Math. Soc.,1,1971, pp.469-474.