A new class of analytic functions associated with the Ruscheweyh derivatives. (English) Zbl 0621.30010

The object of the present paper is to establish several interesting properties and characteristics of the class \({\mathcal A}_{n,p}(a,b)\) of analytic functions, which is introduced here by using the Ruscheweyh derivatives defined in terms of a certain Hadamard product. A relevant problem associated with the general class \({\mathcal A}_{n,p}(a,b)\) is also proposed. This hitherto unresolved problem would generalize one of the results presented here. Finally, it is shown how the class \({\mathcal A}_{n,p}(a,0)\) is related to a certain generalized integral operator studied, for example, by S. Owa and H. M. Srivastava [ibid. 62, 125-128 (1986; Zbl 0583.30016)].


30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)


Zbl 0583.30016
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[1] O. P. Ahuja: On the radius problem of certain analytic functions. Bull. Korean Math. Soc, 22, 31-36 (1985). · Zbl 0573.30009
[2] H. S. Al-Amiri: On Ruscheweyh derivatives. Ann. Polon. Math., 38, 87-94 (1980). · Zbl 0452.30008
[3] H. S. Al-Amiri: On the Ruscheweyh-Mocanu alpha convex functions of order n. Mathematica (Cluj), 22(45), 207-213 (1980). · Zbl 0477.30012
[4] S. D. Bernardi: Convex and starlike univalent functions. Trans. Amer. Math. Soc, 135, 429-446 (1969). · Zbl 0172.09703
[5] T. Bulboaca: Asupra unor noi clase de functii analitice. Studia Univ. Babes-Bolyai Math., 26, 42-46 (1981). · Zbl 0484.30013
[6] S. Fukui and K. Sakaguchi: An extension of a theorem of S. Ruscheweyh. Bull. Fac. Ed. Wakayama Univ. Natur. Sci., 29, 1-3 (1980). · Zbl 1255.30012
[7] R. M. Goel and N. S. Sohi: A new criterion for p-valent functions. Proc. Amer. Math. Soc, 78, 353-357 (1980). · Zbl 0444.30012
[8] R. M. Goel and N. S. Sohi: Subclasses of univalent functions. Tamkang J. Math., 11, 77-81 (1980). · Zbl 0463.30011
[9] R. M. Goel and N. S. Sohi: A new criterion for univalence and its applications. Glasnik Mat. ser. Ill 16(36), 39-49 (1981). · Zbl 0469.30015
[10] V. Kumar and S. L. Shukla: Multivalent functions defined by Ruscheweyh derivatives. Indian J. Pure Appl. Math., 15, 1216-1227 (1984). · Zbl 0567.30012
[11] R. J. Libera: Some classes of regular univalent functions. Proc. Amer. Math. Soc, 16, 755-758 (1965). JSTOR: · Zbl 0158.07702
[12] A. E. Livingston: On the radius of univalence of certain analytic functions, ibid., 17, 352-357 (1966). JSTOR: · Zbl 0158.07701
[13] S. Owa: On the Ruscheweyh’s new criteria for univalent functions. Math. Japonicae, 27, 77-96 (1982). · Zbl 0486.30008
[14] S. Owa: On new criteria for analytic functions. Tamkang J. Math., 13, 201-213 (1982). · Zbl 0515.30011
[15] S. Owa: On a certain class of functions denned by using the Ruscheweyh derivatives. Math. Japonicae, 30, 301-306 (1985). · Zbl 0582.30011
[16] S. Owa and H. M. Srivastava: Some applications of the generalized Libera integral operator. Proc. Japan Acad., 62A, 125-128 (1986). · Zbl 0583.30016
[17] S. Ruscheweyh: New criteria for univalent functions. Proc. Amer. Math. Soc, 49, 109-115 (1975). · Zbl 0303.30006
[18] R. Singh and S. Singh: Integrals of certain univalent functions, ibid., 77, 336-340 (1979). JSTOR: · Zbl 0423.30007
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