Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0583.30016
Owa, Shigeyoshi; Srivastava, H.M.
Some applications of the generalized Libera integral operator. (English)
[J] Proc. Japan Acad., Ser. A 62, 125-128 (1986). ISSN 0386-2194

For a function f(z) belonging to a class A of normalized analytic functions in the unit disc, we define the generalized Libera integral operator $J\sb c$ by $$ J\sb c(f)=((c+1)/z\sp c)\int\sp{z}\sb{0}t\sp{c- 1}f(t)dt\quad (c\ge 0). $$ The operator $J\sb c$, when $c\in N=\{1,2,3,\ldots \}$, was introduced by {\it S. D. Bernardi} [Trans. Am. Math. Soc. 135, 429-446 (1969; Zbl 0172.097)]. In particular, the operator $J\sb 1$ was studied earlier by {\it R. J. Libera} [Proc. Am. Math. Soc. 16, 755-758 (1965; Zbl 0158.077)] and {\it A. E. Livingston} [Proc. Am. Math. Soc. 17, 352-357 (1966; Zbl 0158.077)]. \par The object of the present paper is to prove several interesting characterization theorems involving the generalized Libera integral operator $J\sb c$ and a general class C($\alpha$,$\beta)$ of close-to- convex functions in the unit disc. An application of the integral operator $J\sb c$ to a class of generalized hypergeometric functions is also considered.

MSC 2000:: *30C45 Special classes of univalent and multivalent functions
33C05 Classical hypergeometric functions

Keywords: Libera integral operator; close-to-convex functions

Citations: Zbl 0172.097; Zbl 0158.077

Cited in: Zbl 0741.30013 Zbl 0764.30012 Zbl 0621.30010

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]