We introduce a new class of analytic functions by using the Rafid integral operator and obtain some subordination results.
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A. Akgül, “On second-order differential subordinations for a class of analytic functions defined by convolution,” J. Nonlin. Sci. Appl., 10, No. 3, 954–963 (2017).
W. G. Athsan and R. H. Buti, “Fractional calculus of a class of univalent functions,” Eur. J. Pure Appl. Math., 4, No. 2, 162–173 (2011).
A. Alb. Lupas, “Certain differential subordinations using Sălăgeăn and Ruscheweyh operators,” Acta Univ. Apulensis Math. Inform., No. 29, 125–129 (2012).
S. Bulut, “Some applications of second-order differential subordination on a class of analytic functions defined by Komatu integral operator,” ISRN Math. Anal., No. 5, Art. ID 606235 (2014).
D. J. Hallenbeck and S. Ruscheweyh, “Subordinations by convex functions,” Proc. Amer. Math. Soc., 52 (1975).
S. S. Miller and P. T. Mocanu, “Differential subordinations: theory and applications,” in: Pure Appl. Math. Series Monogr. Textbooks, CRC Press (2000), 225.
G. Oros and G. I. Oros, “A class of holomorphic functions II,” Lib. Math. (N.S.), 23, 65–68 (2003).
G. I. Oros and G. Oros, “On a class of univalent functions defined by a generalized Sălăgean operator,” Complex Var. Elliptic Equat., 53, No. 9, 869–877 (2008).
G. Sălăgean, “Subclass of univalent functions,” in: Complex Anal. (Fifth Romanian-Finnish Sem. Pt 1 (Bucharest, 1981)): Lect. Notes Math., Springer, 1013 (1981), pp. 362–372.
S. S. Miller and P. T. Mocanu, “Second order differential inequalities in the complex plane,” J. Math. Anal. Appl., 65, No. 2, 298–305 (1978).
S. S. Miller and P. T. Mocanu, “Differential subordinations and univalent functions,” Michigan Math. J., 28, No. 2, 157–171 (1981).
T. Bulboacă, “Differential subordinations and superordinations,” in: Recent Results, House Sci. Book Publ., Cluj-Napoca (2005).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 5, pp. 587–598, May, 2018.
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Akgül, A. Second-Order Differential Subordinations on a Class of Analytic Functions Defined by the Rafid Operator. Ukr Math J 70, 673–686 (2018). https://doi.org/10.1007/s11253-018-1525-9
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DOI: https://doi.org/10.1007/s11253-018-1525-9