Janusz SOKOL, Hesam MAHZOON, Rahim KARGAR

A new subclass of starlike functions

Motivated by the Rønning-starlike class [Proceedings of the American Mathematical Society 1993; 118:189-196], we introduce the new class S∗c that includes analytic and normalized functions f , which satisfy the inequality $Re{frac{zf'(z)}{f(z)}}geqleft|frac{f(z)}z-1right|;;(left|zright|

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[1] Ali RM, Ravichandran V, Seenivasagan N. Coefficient bounds for p-valent functions. Applied Mathematics and Computation 2007; 187 (1): 35-46. doi: 10.1016/j.amc.2006.08.100
[2] Duren PL. Univalent Functions. Berlin, Germany: Springer-Verlag, 1983.
[3] Jack IS. Functions starlike and convex of order α. Journal of the London Mathematical Society 1971; 3 (2): 469-474. doi: 10.1112/jlms/s2-3.3.469
[4] Marx A. Untersuchungen über schlichte Abbildungen. Mathematische Annalen 1933; 107 (1): 40-67 (in German).
[5] Miller SS, Mocanu PT. Differential Subordinations, Theory and Applications. Series of Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225. New York, NY, USA: Marcel Dekker, 2000.
[6] Nunokawa M. On properties of non-Carathéodory functions. Proceedings of the Japan Academy, Series A, Mathematical Sciences 1992; 68 (6): 152-153. doi: 10.3792/pjaa.68.152
[7] Prokhorov DV, Szynal J. Inverse coefficients for (α, β) -convex functions. Annales Universitatis Mariae Curie- Sklodowska, Sectio A - Mathematica 1984; 35: 125-143.
[8] Robertson MIS. On the theory of univalent functions. Annals of Mathematics 1936; 37 (2): 374-408. doi: 10.2307/1968451
[9] Rogosinski W. On the coefficients of subordinate functions. Proceedings of the London Mathematical Society 1943; 2 (1): 48-82. doi: 10.1112/plms/s2-48.1.48
[10] Rønning F. Uniformly convex functions and a corresponding class of starlike functions. Proceedings of the American Mathematical Society 1993; 118 (1): 189-196. doi: 10.2307/2160026
[11] Shoikhet D. Semigroups in Geometrical Function Theory. Berlin, Germany: Springer Science & Business Media, 2013.
[12] Strohhäcker E. Beiträge zur Theorie der schlichten Funktionen. Mathematische Zeitschrift 1933; 37 (1): 356-380 (in German).
[13] Tuneski N, Nunokawa M, Jolevska-Tuneska B. A Marx-Strohhacker type result for close-to-convex functions. In: Agranovsky M, Golberg A, Jacobzon F, Shoikhet D, Zalcman L (editors). Complex Analysis and Dynamical Systems. Trends in Mathematics. Basel, Switzerland: Birkhäuser, 2018.

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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