On application of differential subordination for Carathéodory functions

V. Agnes Sagaya Judy Lavanya; M. P. Jeyaraman; H. Aaisha Farzana

doi:10.2478/ausm-2020-0026

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

On application of differential subordination for Carathéodory functions

Acta Universitatis Sapientiae, Mathematica

Volume 12 (2020): Issue 2 (November 2020)

By: V. Agnes Sagaya Judy Lavanya, M. P. Jeyaraman and H. Aaisha Farzana

Open Access

|Dec 2020

Abstract

New sufficient conditions involving the properties of analytic functions to belong to the class of Carathéodory functions are investigated. Certain univalence and starlikeness conditions are deduced as special cases of main results.

References

[1] J. A. Antonino, S. S. Miller, Third-order differential inequalities and subordinations in the complex plane, Complex Var. Elliptic Equ., 56 (5) (2011), 439–454.10.1080/17476931003728404
Open DOI Search in Google Scholar Back to article
[2] P. L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften, 259, Springer-Verlag, New York, 1983.
Search in Google Scholar Back to article
[3] Huo Tang, H. M. Srivastava, Shu-Hai Li, Li-Na Ma, Third-order differential subordination and superordination results for meromorphically multi-valent functions associated with the Liu-Srivastava operator, Abstr. Appl. Anal., 2014, Art. ID 792175, 11 pp.10.1155/2014/792175
Open DOI Search in Google Scholar Back to article
[4] I. S. Jack, Functions starlike and convex of order α, J. London Math. Soc., 3 (2) (1971), 469–474.10.1112/jlms/s2-3.3.469
Open DOI Search in Google Scholar Back to article
[5] I. H. Kim, N. E. Cho, Sufficient conditions for Carathéodory functions, Comput. Math. Appl., 59 (6) (2010), 2067–2073.10.1016/j.camwa.2009.12.012
Open DOI Search in Google Scholar Back to article
[6] I. H. Kim, Y. J. Sim, N. E. Cho, New criteria for Carathéodory functions, J. Inequal. Appl., 13 (2019), 16 pp.10.1186/s13660-019-1970-5
Open DOI Search in Google Scholar Back to article
[7] S. Miller, Differential inequalities and Carathéodory functions, Bull. Amer. Math. Soc., 81 (1975), 79–81.10.1090/S0002-9904-1975-13643-3
Open DOI Search in Google Scholar Back to article
[8] S. S. Miller, P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J., 28 (2) (1981), 157–172.10.1307/mmj/1029002507
Open DOI Search in Google Scholar Back to article
[9] S. S. Miller, P. T. Mocanu, Differential subordinations, Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., New York, 2000.
Search in Google Scholar Back to article
[10] S. S. Miller, P. T. Mocanu, M. O. Reade, All α-convex functions are starlike, Rev. Roumaine Math. Pures Appl., 17 (1972), 1395–1397.
Search in Google Scholar Back to article
[11] N. Xu, Sufficient conditions and applications for Carathéodory functions, J. Math., 2013, Art. ID 930290, 4 pp.10.1155/2013/930290
Open DOI Search in Google Scholar Back to article
[12] M. Nunokawa, Differential inequalities and Carathéodory functions, Proc. Japan Acad. Ser. A Math. Sci., 65 (10) (1989), 326–328.10.3792/pjaa.65.326
Open DOI Search in Google Scholar Back to article
[13] M. Nunokawa, A. Ikeda, N. Koike, Y. Ota, H. Saitoh, Differential inequalities and Carathéodory functions, J. Math. Anal. Appl., 212 (1) (1997), 324–332.10.1006/jmaa.1997.5519
Open DOI Search in Google Scholar Back to article
[14] M. Nunokawa, S. Owa, N. Takahashi, H. Saitoh, Sufficient conditions for Carathéodory functions, Indian J. Pure Appl. Math., 33 (9) (2002), 1385–1390.
Search in Google Scholar Back to article
[15] M. Nunokawa, M. Obradović, S. Owa, One criterion for univalency, Proc. Amer. Math. Soc., 106 (4) (1989), 1035–1037.10.1090/S0002-9939-1989-0975653-5
Open DOI Search in Google Scholar Back to article
[16] S. Ponnusamy, P. Vasundhra, Starlikeness of nonlinear integral transforms, J. Anal., 15 (2007), 195–210.
Search in Google Scholar Back to article
[17] J. Sokół, On some subclass of strongly starlike functions, Demonstratio Math., 31 (1) (1998), 81–86.10.1515/dema-1998-0111
Open DOI Search in Google Scholar Back to article
[18] J. Sokół, J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej, 19 (1996), 101– 105.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/ausm-2020-0026 | Journal eISSN: 2066-7752

Journal RSS Feed

Language: English

Page range: 370 - 382

Submitted on: Jul 4, 2020

Published online: Dec 2, 2020

Published in print: Nov 1, 2020

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

analytic functions,

differential subordination,

Carathéodory function,

starlike function,

univalent function

MSC:

30C45,

30C80

Related subjects:

Mathematics,

General mathematics

© 2020 V. Agnes Sagaya Judy Lavanya, M. P. Jeyaraman, H. Aaisha Farzana, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 12 (2020): Issue 2 (November 2020)