zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
On a generalization of uniformly convex and related functions. (English) Zbl 1207.30023
Summary: We define and study some subclasses of analytic functions by using the concept of k-uniformly convexity. Several interesting properties, coefficients and radius problems are investigated. The behaviour of these classes under a certain integral operator is also studied. We indicate the relevant connections of our results with various known ones.
MSC:
30C45Special classes of univalent and multivalent functions
References:
[1]Goodman, A. W.: Univalent functions, Univalent functions & II (1983)
[2]Kanas, S.; Wisniowska, A.: Conic regions and k-uniform convexity, II, Zeszyty nauk. Politech. rzeszowskiej mat. 170, No. 22, 65-78 (1998) · Zbl 0995.30013
[3]Kanas, S.; Wisniowska, A.: Conic regions and k-uniform convexity, J. comput. Appl. math. 105, 327-336 (1999) · Zbl 0944.30008 · doi:10.1016/S0377-0427(99)00018-7
[4]Kanas, S.: Techniques of the differential subordination for domains bounded by conic sections, Int. J. Math. math. Sci. 38, 2389-2400 (2003) · Zbl 1130.30307 · doi:10.1155/S0161171203302212
[5]Noor, K. Inayat; Arif, M.; Ul-Haq, W.: On k-uniformly close-to-convex functions of complex order, Appl. math. Comput. 215, 629-635 (2009) · Zbl 1176.30050 · doi:10.1016/j.amc.2009.05.050
[6]Kanas, S.; Lecko, A.: Differential subordination for domains bounded by hyperbolas, Zeszyty nauk. Politech. rzeszowskiej mat. 175, No. 23, 61-70 (1999) · Zbl 1074.30504
[7]S. Kanas, Coefficient estimates in subclasses of the Caratheodory class related to conical domains, Acta Sci. Math. (in press). · Zbl 1138.30301 · doi:emis:journals/AMUC/_vol-74/_no_2/_kanas/kanas.html
[8]S. Kanas, Subclasses of the Caratheodory class related to conical domains, Georgian Math. (in press).
[9]Pinchuk, B.: Functions with bounded boundary rotation, Israel J. Math. 10, 7-16 (1971) · Zbl 0224.30024 · doi:10.1007/BF02771515
[10]Noor, K. Inayat: Some properties of analytic functions with bounded radius rotation, Complex var. Elliptic equ. 54, 865-877 (2009) · Zbl 1176.30049 · doi:10.1080/17476930902998878
[11]Noor, K. Inayat; Ul-Haq, W.; Arif, M.; Mustafa, S.: On bounded boundary and bounded radius rotation, J. inequal. Appl. 2009 (2009) · Zbl 1176.30047 · doi:10.1155/2009/813687
[12]Noor, K. Inayat: Some recent developments in the theory of functions with bounded boundary rotations, Inst. math. Comput. sci. 2, 25-37 (2007)
[13]Ronning, F.: Uniformly convex functions and a corresponding class of starlike functions, Proc. amer. Math. soc. 118, 189-196 (1993) · Zbl 0805.30012 · doi:10.2307/2160026
[14]Brannan, D. A.: On functions of bounded boundary rotations, Proc. edinb. Math. soc. 2, 339-347 (1968–1969)
[15]Noor, K. Inayat: Higher order close-to-convex functions, Math. japon. 37, 1-8 (1992) · Zbl 0745.30016
[16]Noor, K. Inayat: On analytic functions related with functions of bounded boundary rotation, Comment math. Univ. st. Pauli 30, 113-118 (1981) · Zbl 0473.30009
[17]Ronning, F.: Some radius results for univalent functions, J. math. Anal. appl. 194, 319-327 (1995) · Zbl 0834.30011 · doi:10.1006/jmaa.1995.1301
[18]Golusion, G.: On distortion theorems and coefficients of univalent functions, Math. sb. 19, 183-203 (1946) · Zbl 0063.01668
[19]Noor, K. Inayat: On some subclasses of functions with bounded radius and bounded boundary rotation, Panamer. math. J. 6, 1-7 (1996) · Zbl 0966.30007