New applications in third-order strong differential subordination theory
Year 2024,
Volume: 73 Issue: 4, 918 - 928
Lavinia Florina Preluca
,
Georgia Irina Oros
Abstract
The research conducted in this investigation focuses on extending known results from the second-order differential subordination theory for the special case of third-order strong differential subordination. This paper intends to facilitate the development of new results in this theory by showing how specific lemmas used as tools in classical second-order differential subordination theory are adapted for the context of third-order strong differential subordination. Two theorems proved in this study extend two familiar lemmas due to D.J. Hallenbeck and S. Ruscheweyh, and G.M. Goluzin, respectively. A numerical example illustrates applications of the new results but the theorems are hoped to become helpful tools in generating new outcome for this very recently initiated line of research concerning third-order strong differential subordination.
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Year 2024,
Volume: 73 Issue: 4, 918 - 928
Lavinia Florina Preluca
,
Georgia Irina Oros
References
- Antonino, J.A., Miller, S.S., Third-order differential inequalities and subordinations in the complex plane, Complex Var. Elliptic Equ., 56(5) (2011), 439-454. https://doi.org/10.1080/17476931003728404
- Miller, S.S., Mocanu, P.T., Second order-differential inequalities in the complex plane, J. Math. Anal. Appl., 65 (1978), 298–305. https://doi.org/10.1016/0022-247X(78)90181-6
- Miller, S.S., Mocanu, P.T., Differential subordinations and univalent functions, Michig. Math. J., 28 (1981), 157–171. https://doi.org/10.1307/mmj/1029002507
- Zayed, H.M., Bulboac˘a, T., Applications of differential subordinations involving a generalized fractional differintegral operator, J. Inequal. Appl., 2019 (2019), 242. https://doi.org/10.1186/s13660-019-2198-0
- Atshan, W.G., Hiress, R.A., Altınkaya, S., On third-order differential subordination and superordination properties of analytic functions defined by a generalized operator, Symmetry, 14 (2022), 418. https://doi.org/10.3390/sym14020418
- Al-Janaby, H., Ghanim, F., Darus, M., On the third-order complex differential inequalities of ξ-generalized-Hurwitz–Lerch zeta functions, Mathematics, 8 (2020), 845. https://doi.org/10.3390/math8050845
- Attiya, A.A., Seoudy, T.M., Albaid, A., Third-order differential subordination for meromorphic functions associated with generalized Mittag-Leffler function, Fractal Fract., 7 (2023), 175. https://doi.org/10.3390/fractalfract7020175
- Oros, G.I., Oros, G., Preluca, L.F., Third-order differential subordinations using fractional integral of Gaussian hypergeometric function, Axioms, 12 (2023), 133. https://doi.org/10.3390/axioms12020133
- Oros, G.I., Oros, G., Preluca, L.F., New applications of Gaussian hypergeometric function for developments on third-order differential subordinations, Symmetry, 15 (2023), 1306. https://doi.org/10.3390/sym15071306
- Soren, M.M., Wanas, A.K., Cotirla, L.-I., Results of third-order strong differential subordinations, Axioms, 13 (2024), 42. https://doi.org/10.3390/axioms13010042
- Oros, G.I., Oros, G., Strong differential subordination, Turk. J. Math., 33 (2009), 249–257. https://doi.org/10.3906/mat-0804-16
- Antonino, J.A., Romaguera, S., Strong differential subordination to Briot-Bouquet differential equations, J. Differ. Equ., 114 (1994), 101–105. https://doi.org/10.1006/jdeq.1994.1142
- Oros, G.I., On a new strong differential subordination, Acta Univ. Apulensis, 32 (2012), 243–250.
- Wanas, A.K., Frasin, B.A., Strong differential sandwich results for Frasin operator, Earthline J. Math. Sci., 3 (2020), 95–104. https://doi.org/10.34198/ejms.3120.95104
- Arjomandinia, P., Aghalary, R., Strong subordination and superordination with sandwichtype theorems using integral operators, Stud. Univ. Babe¸s-Bolyai Math., 66 (2021), 667–675. http://dx.doi.org/10.24193/subbmath.2021.4.06
- Alb Lupa¸s, A., Applications of a Multiplier Transformation and Ruscheweyh Derivative for Obtaining New Strong Differential Subordinations, Symmetry, 13 (2021), 1312. https://doi.org/10.3390/sym13081312
- Aghalary, R., Arjomandinia, P., On a first order strong differential subordination and application to univalent functions, Commun. Korean Math. Soc., 37 (2022), 445–454. https://doi.org/10.4134/CKMS.c210070
- Alb Lupa¸s, A., Ghanim, F., Strong differential subordination and superordination results for extended q-analogue of multiplier transformation, Symmetry, 15 (2023), 713. https://doi.org/10.3390/sym15030713
- Tang, H., Srivastava, H.M., Li, S.-H., Ma, L., Third-order differential subordination and superordination results for meromorphically multivalent functions associated with the Liu-Srivastava operator, Abstr. Appl. Anal., 2014 (2014), 1–11. https://doi.org/10.1155/2014/792175
- Hallenbeck, D.J., Ruscheweyh, S., Subordination by convex functions, Proc. Amer. Math. Soc., 52 (1975), 191–195. https://doi.org/10.2307/2040127
- Goluzin, G.M., On the majorization principle in function theory, (in Russian) Dokl. Akad. Nauk SSSR, 42 (1935), 647-650.
- Suffridge, T.J., Some remarks on convex maps of the unit disc, Duke Math. J., 37 (1970), 775–777. https://doi.org/10.1215/S0012-7094-70-03792-0