Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

Rabha W. Ibrahim

doi:10.2478/gm-2020-0008

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

Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

General Mathematics

Volume 28 (2020): Issue 1 (June 2020)

By: Rabha W. Ibrahim

Open Access

|Jul 2020

Abstract

Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

References

[1] A. A. Lupas, On special differential subordinations using Salagean and Ruscheweyh operators, Math. Inequal. Appl., vol. 12, no. 4, 2009, 781–790.10.7153/mia-12-61
Search in Google Scholar Back to article
[2] A. A. Lupas, Some differential subordinations using Ruscheweyh derivative and Salaagean operator, Advances in Difference Equations, vol. 2013, no. 150, 2013, 1–12.
Search in Google Scholar Back to article
[3] N. E. Cho, et al., Radius problems for starlike functions associated with the sine function, Bull. Iran. Math. Soc., vol.45, no.213, 2019, 1–20.10.1007/s41980-018-0127-5
Search in Google Scholar Back to article
[4] C. F. Dunkl, Differential-difference operators associated with reflections groups, Trans. Am. Math. Soc., vol. 311, 1989, 167–183.10.1090/S0002-9947-1989-0951883-8
Search in Google Scholar Back to article
[5] P. Duren, Univalent Functions, Grundlehren der mathematischen Wissenschaften; 259 Springer-Verlag New York Inc., 1983.
Search in Google Scholar Back to article
[6] R. W. Ibrahim, M. Darus, Subordination inequalities of a new Salagean-difference operator, International Journal of Mathematics and Computer Science, vol. 14, no. 3, 2019, 573–582.
Search in Google Scholar Back to article
[7] S. Kanas, A. Wisniowska, Conic domains and starlike functions, Rev. Roum. Math. Pures Appl., vol. 45, no. 4, 2000, 647–657.
Search in Google Scholar Back to article
[8] K. Khatter, et al., Starlike functions associated with exponential function and the lemniscate of Bernoulli, Revista de la Real Academia de Ciencias Exactas, Serie A. Matematicas, vol. 113, no. 1, 2019, 233–253.10.1007/s13398-017-0466-8
Search in Google Scholar Back to article
[9] V. Kumar, et al., Sharp coefficient bounds for starlike functions associated with the Bell numbers, Math. Slovaca, vol. 69, 2019, 1053–1064.10.1515/ms-2017-0289
Search in Google Scholar Back to article
[10] W. C. Ma, D. Minda, A unified treatment of some special classes of univalent functions, In Proceedings of the Conference on Complex Analysis, Tianjin, China, vol. 19, no. 23, 1992, 1–13.
Search in Google Scholar Back to article
[11] R. Mendiratta, S. Nagpal., V. Ravichandran, On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc., vol. 38, 2015, 365–386.10.1007/s40840-014-0026-8
Search in Google Scholar Back to article
[12] S. S. Miller, P. T. Mocanu, Differential subordinations: theory and applications, CRC Press, 2000.10.1201/9781482289817
Search in Google Scholar Back to article
[13] S. Ruscheweyh, New criteria for univalent functions, Proc. Amet. Math. Soc., vol. 49, 1975, 109–115.10.1090/S0002-9939-1975-0367176-1
Search in Google Scholar Back to article
[14] G. St. Sălăgean, Subclasses of univalent functions, Lecture Notes in Math., Springer Verlag, Berlin, vol. 1013, 1983, 362–372.
Search in Google Scholar Back to article
[15] B. A. Uralegaddi, et al., Univalent functions with positive coefficients, Tamkang J. Math., vol. 25, no. 3, 1994, 225–230.10.5556/j.tkjm.25.1994.4448
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/gm-2020-0008 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023

Journal RSS Feed

Language: English

Page range: 105 - 114

Submitted on: Jul 4, 2019

Accepted on: Apr 30, 2020

Published on: Jul 31, 2020

Published by: Lucian Blaga University of Sibiu

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Differential operator,

Related subjects:

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics,

Applied mathematics

© 2020 Rabha W. Ibrahim, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 28 (2020): Issue 1 (June 2020)