We obtain subordination, superordination and sandwich-preserving new theorems for certain integral operators defined on multivalent functions. The sandwich-type theorem for these integral operators is also derived. Moreover, our results extend some earlier results. Combining these new theorems with some previous related results, we give interesting subordination and superordination consequences for a wide class of analytic integral operators.
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References
T. Bulboacă, “Integral operators that preserve the subordination,” Bull. Korean Math. Soc., 32, 627–636 (1997).
T. Bulboacă, “On a class of integral operators that preserve the subordination,” Pure Math. Appl. (PU.M.A.), 13, 87–96 (2002).
T. Bulboacă, “A class of superordination-preserving integral operators,” Indag. Math. (N.S.), 13, 301–311 (2002).
T. Bulboacă, “Sandwich-type theorems for a class of integral operators,” Bull. Belg. Math. Soc. Simon Stevin, 13, No. 3, 537–550 (2006).
T. Bulboacă, “Sandwich-type results for a class of convex integral operators,” Acta Math. Sci. Ser. B (Engl. Ed.), 32, No. 3, 989–1001 (2012).
N. E. Cho and T. Bulboacă, “Subordination and superordination properties for a class of integral operators,” Acta Math. Sin. (Engl. Ser.), 26, No. 3, 515–522 (2010).
T. H. Gronwall, “Some remarks on conformal representation,” Ann. of Math. (2), 16, No. 1-4, 72–76 (1914–1915).
S. S. Miller and P. T. Mocanu, “Differential subordinations and univalent functions,” Michigan Math. J., 28, No. 2, 157–172 (1981).
S. S. Miller and P. T. Mocanu, “Univalent solutions of Briot–Bouquet differential equations,” J. Different. Equat., 56, No. 3, 297–309 (1985).
S. S. Miller and P. T. Mocanu, “Integral operators on certain classes of analytic functions,” Univalent Functions, Fractional Calculus and their Applications (Kōriyama, 1988), Ellis Horwood Ser. Math. Appl., Horwood, Chichester (1989), p. 153–166.
S. S. Miller and P. T. Mocanu, “Classes of univalent integral operators,” J. Math. Anal. Appl., 157, No. 1, 147–165 (1991).
S. S. Miller and P. T. Mocanu, “Differential subordinations. Theory and applications,” Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., New York (2000).
S. S. Miller and P. T. Mocanu, “Subordinants of differential superordinations,” Complex Var. Theory Appl., 48, No. 10, 815–826 (2003).
Ch. Pommerenke, Univalent Functions, Studia Mathematica/Mathematische Lehrbü cher, Band XXV, Vandenhoeck & Ruprecht, Göttingen (1975).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 6, pp. 749–762, June, 2021. Ukrainian DOI: 10.37863/umzh.v73i6.437.
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Aouf, M.K., Bulboacă, T. & Seoudy, T.M. Integral Operators Preserving Subordination and Superordination for Multivalent Functions. Ukr Math J 73, 872–887 (2021). https://doi.org/10.1007/s11253-021-01965-4
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DOI: https://doi.org/10.1007/s11253-021-01965-4