Certain theorems involving differential superordination and sandwich-type results
DOI:
https://doi.org/10.24193/subbmath.2024.3.05Keywords:
Analytic function, differential superordination, Φ-like function, starlike function, close-to-convex function.Abstract
To obtain the main result of the present paper, we use the
technique of differential superordination. As special cases of our main
result, we obtain sufficient conditions for f ∈ A to be Φ-like, parabolic
Φ-like, starlike, parabolic starlike, close-to-convex and uniform close-to-
convex. We also obtain sandwich-type results regarding these functions.
For demonstration of the results, we have plotted the images of open
unit disk under certain functions using Mathematica 7.0.
References
Adegani, E.A., Bulboaca T., Motamednezhad, A., Simple sufficient subordination conditions for close-to-convexity, Mathematics, 7(2019), no. 3.
Brickman, L., Φ-like analytic functions, I, Bull. Amer. Math. Soc., 79(1973), 555-558.
Bulboaca T., Differential subordinations and superordinations: Recent results, House of science Book Publ., Cluj-Napoca 2005.
Kaur, H., Brar, R. and Billing, S.S., Certain Sufficient Conditions for Φ-like Functions in a Parabolic Region, Studia Universitatis Babes-Bolyai Mathematica, (Accepted).
Kaur, P., Billing, S.S., Some sandwich type results for Φ-like functions, Acta Univer. Apul., 51(2017), 115-134.
Rabha, W. Ibrahim, On certain univalent class associated with first order differential subordinations, Tamkang Journal of Mathematics, 42(2011), no. 4, 445-451.
Shanmugam, T.N., Sivassubramanian, S. and Darus Maslina, Subordination and superordination results for Φ-like functions, Journal of ineq. in pure and applied mathematics, 8(2007), no. 1, Art.20, 1-6.
Ma, W. C. and Minda, D., Uniformly convex functions, Ann. Polon. Math., 57(1992), no. 2, 165-175.
Miller, S. S. and Mocanu, P. T., Differential Subordinations: Theory and Applications, Marcel Dekker, New York and Basel, 2000.
Ravichandran, V., Mahesh, N. and Rajalakshmi, R., On Certain Applications of Differential Subordinations for Φ-like Functions, Tamkang J. Math., 36(2005), no. 2, 137-142.
Ronning, F., Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1993), no. 1, 189-196.
Ruscheweyh, St., A subordination theorem for Φ-like functions, J. London Math. Soc., 2(1976), no. 13, 275-280.
Shanmugam, T.N., Sivassubramanian, S., Darus, M.,
Subordination and superordination results for phi-like functions,
Journal of Ineq. in Pure and Applied Mathematics, 8(2007), no. 1, Art. 20, 1-6.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.
