JOURNAL BROWSE
Search
Advanced SearchSearch Tips
New Sufficient Conditions for Starlikeness of Certain Integral Operator
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 1,  2015, pp.109-118
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.1.109
 Title & Authors
New Sufficient Conditions for Starlikeness of Certain Integral Operator
Mishra, Akshaya Kumar; Panigrahi, Trailokya;
  PDF(new window)
 Abstract
In the present paper, a new analytic function valued integral operator is introduced which is defined on n-copies of a subset of the class of normalized analytic functions on the unit disc of the complex plane. This operator, which is denoted here by , unifies and generalizes several integral operators studied earlier. Interesting sufficient conditions are derived for the univalent starlikeness of .
 Keywords
Analytic functions;Integral operator;Starlike functions;
 Language
English
 Cited by
 References
1.
D. Breaz and N. Breaz, Two integral operators, Studia Univ. Babes-Bolyai, Mathematica, Cluj-Napoca, 47(3)(2002),13-19.

2.
D. Breaz and N. Breaz, Univalence conditions for certain integral operators, Studia Univ. Babes-Bolyai, Mathematica, Cluj-Napoca, 47(2)(2002), 9-15.

3.
N. Breaz, D. Breaz and M. Darus, Convexity properties for some general integral operators on uniformly analytic functions classes, Comput. Math. Appl., 60(12)(2010), 3105-3107. crossref(new window)

4.
D. Breaz, N. Breaz and H. M. Srivastava, An extension of the univalent condition for a family of integral operators, Appl. Math. Lett., 22(2009), 41-44. crossref(new window)

5.
D. Breaz, S. Owa and N. Breaz, A new integral univalent operator, Acta Univ. Apul., 16(2008), 11-16.

6.
E. Deniz, H. Orhan and H. M. Srivastava, Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math., 15(2)(2011), 883-917.

7.
M. Dorf and J. Szynal, Linear invariance and integral operators of univalent functions, Demonstratio Math., 38(1)(2005), 47-57.

8.
P. L. Duren, Univalent Functions, Graduate Texts in Mathematics; 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokoyo (1983).

9.
B. A. Frasin, B. S. Keerthi, V. G. Shanthi and B. A. Stephen, Starlikeness and subordination of two integral operators, Thai J. Math., 8(1)(2010), 141-148.

10.
S. Kanas and H. M. Srivastava, Some criteria for univalence related to Ruscheweyh and Salagean derivatives, Complex Variales Theory Appl., 38(1999), 263-275. crossref(new window)

11.
S. S. Miller, P. T. Mocanu and M. O. Reade, Starlike integral operators, Pacific J. Math., 79(1)(1978), 157-168. crossref(new window)

12.
A. Mohammed and M. Darus, Some properties of certain integral operators on new subclasses of analytic functions with complex order, J. Appl. Math., 2012(2012), Art. ID 161436.

13.
A. Mohammed and M. Darus, New properties for certain integral operators, Int. J. Math. Anal., 4(2010), 2101-2109.

14.
A. Mohammed and M. Darus, A new integral operator for meromorphic functions, Acta Univ. Apul., 24(2010), 231-238.

15.
N. Pascu and V. Pescar, On the integral operators of Kim-Merkis and Pfaltzgraff, Mathematica, 32(1990), 185-192.

16.
V. Pescar, On univalence of an integral operator, Novi Sad J. Math., 40(2010), 29-36.

17.
H. Shiraishi and S. Owa, Starlikeness and convexity for analytic functions concerned with Jack's lemma, Int. J. Open Problems Comput. Math., 2(1)(2009), 37-47.

18.
H. M. Srivatava, E. Deniz and H. Orhan, Some general univalence criteria for a family of integral operators, Appl. Math. Comput., 215(2010), 3696-3701. crossref(new window)

19.
L. F. Stanciu, D. Breaz and H. M. Srivastava, Some criteria for univalence of a certain integral operator, Novi Sad J. Math., 43(2)(2013), 51-57.