commun. fac. sci. univ. ank. ser. a1 math. stat. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 1303-5991 2618-6470 Ankara University 10.31801/cfsuasmas.1475919 Real and Complex Functions (Incl. Several Variables) Reel ve Kompleks Fonksiyonlar New applications in third-order strong differential subordination theory https://orcid.org/0000-0001-9215-2404 Preluca Lavinia Florina University of Oradea https://orcid.org/0000-0003-2902-4455 Oros Georgia Irina University of Oradea 12 30 2024 73 4 918 928 04 30 2024 09 02 2024 Copyright © 1948, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 1948 Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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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