On partial sums of normalized Mittag-Leffler functions

Dorina Răducanu

doi:10.1515/auom-2017-0024

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

On partial sums of normalized Mittag-Leffler functions

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 25 (2017): Issue 2 (July 2017)

By: Dorina Răducanu

Open Access

|Sep 2017

Abstract

This article deals with the ratio of normalized Mittag-Leffler function E_α,β(z) and its sequence of partial sums (E_α,β)_m(z). Several examples which illustrate the validity of our results are also given.

References

[1] D. Bansal, J. K. Prajapat, Certain geometric properties of the Mittag-Leffler functions, Complex Var. Elliptic Equ., 61(3)(2016), 338-350.10.1080/17476933.2015.1079628
Search in Google Scholar Back to article
[2] M. Çağlar, E. Deniz, Partial sums of the normalized Lommel functions, Math. Inequal. Appl., 18(3)(2015), 1189-1199.10.7153/mia-18-92
Search in Google Scholar Back to article
[3] M. Din, M. Raza, N. Ya_gmur, Partial sums of normalized Wright functions , arXiv:1606.02750v1 [math.CV], 2016.10.1155/2016/1896154
Search in Google Scholar Back to article
[4] B. A. Frasin, Generalization of partial sums of certain analytic and univalent functions, Appl. Math. Lett., 21(2008), 735-741.10.1016/j.aml.2007.08.002
Open DOI Search in Google Scholar Back to article
[5] A. W. Goodman, Univalent functions, vol. I, Mariner Publishing Company, Inc., 1983.
Search in Google Scholar Back to article
[6] R. Goreno, F. Mainardi, S. V. Rogosin, On the generalized Mittag-Leffler type function, Integral Transform. Spec. Funct., 7(1998), 215-224.10.1080/10652469808819200
Search in Google Scholar Back to article
[7] I. S. Gupta, L. Debnath, Some properties of the Mittag-Leffler functions, Integral Transform. Spec. Funct., 18(5)(2007), 329-336.10.1080/10652460601090216
Search in Google Scholar Back to article
[8] L. J. Liu, S. Owa, On partial sums of the Libera integral operator, J. Math. Anal. Appl., 213(2)(1997), 444-454.10.1006/jmaa.1997.5549
Search in Google Scholar Back to article
[9] G. M. Mittag-Leffler, Sur la nouvelle fonction E_(x), C. R. Acad. Sci. Paris, 137(1903), 554-558.
Search in Google Scholar Back to article
[10] H. Orhan, N. Ya_gmur, Partial sums of generalized Bessel functions, J. Math. Inequal., 8(4)(2014), 863-877.10.7153/jmi-08-65
Search in Google Scholar Back to article
[11] S. Owa, H. M. Srivastava, N. Saitoh, Partial sums of certain classes of analytic functions, Int. J. Comput. Math., 81(10)(2004), 1239-1256.10.1080/00207160412331284042
Search in Google Scholar Back to article
[12] T. R. Prabhakar, A singular integral equation with a generalized Mittag- Leffler function in the kernel, Yokohama Math. J., 19(1997), 7-15.
Search in Google Scholar Back to article
[13] V. Ravichandran, Geometric properties of partial sums of univalent functions , Math. Newslett., 22(3)(2012), 208-221.
Search in Google Scholar Back to article
[14] D. Răducanu, Differential subordinations associated with generalized Mittag-Leffler functions (submitted).
Search in Google Scholar Back to article
[15] T. O. Salim, Some properties relating to the generalized Mittag-Leffler function, Advances Appl. Math. Anal., 4(1)(2009), 21-30.
Search in Google Scholar Back to article
[16] A. K. Shukla, J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties, J. Math. Anal. Appl., 337(2007), 797-811.10.1016/j.jmaa.2007.03.018
Search in Google Scholar Back to article
[17] H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl., 209(1997), 221-227.10.1006/jmaa.1997.5361
Search in Google Scholar Back to article
[18] E. M. Silvia, On partial sums of convex functions of order , Houston J. Math., 11(1985), 397-404.
Search in Google Scholar Back to article
[19] A. E. Tudor, D. Răducanu, On a subclass of analytic functions involving harmonic means, An. S_t. Univ. Ovidius Constant_a, 23(1)(2015), 267-275.10.1515/auom-2015-0018
Search in Google Scholar Back to article
[20] A. Wiman, Über den Fundamental satz in der Theorie der Funcktionen E_(x), Acta Math., 29(1905), 191-201.10.1007/BF02403202
Open DOI Search in Google Scholar Back to article
[21] A. Wiman, Über die Nullstellun der Funcktionen E_(x), Acta Math., 29(1905), 217-134.10.1007/BF02403204
Open DOI Search in Google Scholar Back to article
[22] N. Yağmur, H. Orhan, Partial sums of generalized Struve functions, Miskolc. Math. Notes (accepted.)
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/auom-2017-0024 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 123 - 133

Submitted on: Jul 1, 2016

Accepted on: Sep 21, 2016

Published on: Sep 21, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Analytic functions,

partial sums,

Mittag-Leffler function,

univalent function

Related subjects:

Mathematics,

General mathematics

© 2017 Dorina Răducanu, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 25 (2017): Issue 2 (July 2017)