zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Some inclusion properties of a certain family of integral operators. (English) Zbl 1035.30004
{\it K. I. Noor} [J. Nat. Geom. 16, 71--80 (1999; Zbl 0942.30007)] introduced and studied a new class of integral operators associated with analytic functions. This operator is known as Noor integral operator. In this paper, the authors have considered some new classes of analytic functions defined by the generalized Noor integral operator. Using the standard technique, the authors have studied some inclusion properties of these classes. For recent research work on the Noor integral operator, see {\it K. I. Noor} and {\it M. A. Noor}, J. Math. Anal. Appl. 281, 244--252 (2003; Zbl 1022.30018) and {\it N. E. Cho}, J. Math. Anal. Appl. 283, 202--212 (2003; Zbl 1027.30043)]. Also see {\it K. I. Noor}, N. Z. J. Math. 24, 53--64 (1995; Zbl 0841.30012), where the linear operator was defined using the hypergeometric function.

30C45Special classes of univalent and multivalent functions
30C80Maximum principle; Schwarz’s lemma, Lindelöf principle, etc. (one complex variable)
Full Text: DOI
[1] Bernardi, S. D.: Convex and starlike univalent functions. Trans. amer. Math. soc. 135, 429-446 (1969) · Zbl 0172.09703
[2] Carlson, B. C.; Shaffer, D. B.: Starlike and prestarlike hypergeometric functions. SIAM J. Math. anal. 15, 737-745 (1984) · Zbl 0567.30009
[3] Eenigenburg, P.; Miller, S. S.; Mocanu, P. T.; Reade, M. O.: On a briot--bouquet differential subordination. International series of numerical mathematics 64, 339-348 (1983) · Zbl 0527.30008
[4] Goel, R. M.; Mehrok, B. S.: On the coefficients of a subclass of starlike functions. Indian J. Pure appl. Math. 12, 634-647 (1981) · Zbl 0456.30016
[5] Janowski, W.: Some extremal problems for certain families of analytic functions. Bull. acad. Polon. sci. Sér. sci. Math. astronom. Phys. 21, 17-25 (1973) · Zbl 0252.30021
[6] Kim, Y. C.; Choi, J. H.; Sugawa, T.: Coefficient bounds and convolution properties for certain classes of close-to-convex functions. Proc. Japan acad. Ser. A math. Sci. 76, 95-98 (2000) · Zbl 0965.30006
[7] Libera, R. J.: Some classes of regular univalent functions. Proc. amer. Math. soc. 16, 755-758 (1965) · Zbl 0158.07702
[8] Liu, J. -L.: The Noor integral and strongly starlike functions. J. math. Anal. appl. 261, 441-447 (2001) · Zbl 1040.30005
[9] Liu, J. -L.; Noor, K. I.: Some properties of Noor integral operator. J. natur. Geom. 21, 81-90 (2002) · Zbl 1005.30015
[10] Ma, W.; Minda, D.: A unified treatment of some special classes of univalent functions. Proceedings of the conference on complex analysis, 157-169 (1992) · Zbl 0823.30007
[11] Miller, S. S.; Mocanu, P. T.: Differential subordinations and inequalities in the complex plane. J. differential equations 67, 199-211 (1987) · Zbl 0633.34005
[12] Noor, K. I.: On new classes of integral operators. J. natur. Geom. 16, 71-80 (1999) · Zbl 0942.30007
[13] Noor, K. I.; Noor, M. A.: On integral operators. J. math. Anal. appl. 238, 341-352 (1999) · Zbl 0934.30007
[14] Owa, S.: On the distortion theorems. I. Kyungpook math. J. 18, 53-59 (1978) · Zbl 0401.30009
[15] Owa, S.; Srivastava, H. M.: Univalent and starlike generalized hypergeometric functions. Canad. J. Math. 39, 1057-1077 (1987) · Zbl 0611.33007
[16] Ruscheweyh, S.: New criteria for univalent functions. Proc. amer. Math. soc. 49, 109-115 (1975) · Zbl 0303.30006
[17] Srivastava, H. M.; Owa, S.: Univalent functions, fractional calculus, and their applications. (1989) · Zbl 0683.00012
[18] Srivastava, H. M.; Owa, S.: Current topics in analytic function theory. (1992) · Zbl 0976.00007