Certain sufficient conditions for φ -like functions in a parabolic region
DOI:
https://doi.org/10.24193/subbmath.2023.2.05Keywords:
Analytic function, differential subordination, parabolic φ like function, parabolic starlike function, close-to-convex function.Abstract
To obtain the main result of the present paper we use the technique of differential subordination. As special cases of our main result, we obtain sufficient conditions for \(f\in A\) to be φ -like, starlike and close-to-convex in a parabolic region.
Mathematics Subject Classification (2010): 30C80, 30C45.
Received 21 May 2020; Accepted 21 July 2020.
References
L. Brickman, φ like analytic functions, I, Bull. Amer. Math. Soc., 79 (1973), 555-558.
W. C. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math., 57 (1992), no. 2, 165-175.
S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Marcel Dekker, New York and Basel (2000).
Rabha W. Ibrahim, On certain univalent class associated with first order differential sub- ordinations, Tamkang Journal of Mathematics, 42, 4(2011), 445-451.
V. Ravichandran, N. Mahesh and R. Rajalakshmi, On Certain Applications of Differential Subordinations for φ-like Functions, Tamkang J. Math., 36, 2 (2005), 137-142.
F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118, (1993), no. 1, 189-196.
St. Ruscheweyh, A subordination theorem for φ-like functions, J. London Math. Soc., 2, 13 (1976), 275-280.
T.N. Shanmugam, S. Sivassubramanian and Maslina Darus, Subordination and superordination results for φ-like functions, Journal of ineq. in pure and applied mathematics, 8, 1(2007), Art.20, 1-6.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Studia Universitatis Babeș-Bolyai Mathematica
![Creative Commons License](http://i.creativecommons.org/l/by-nc-nd/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.