Taiwanese Journal of Mathematics


Jacek Dziok

Full-text: Open access


By using functions of bounded variation we generalize the class of strongly starlike functions and related classes. The main object is to obtain characterizations and inclusion properties of these classes of functions.

Article information

Taiwanese J. Math., Volume 18, Number 1 (2014), 39-51.

First available in Project Euclid: 10 July 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30C50: Coefficient problems for univalent and multivalent functions 30C55: General theory of univalent and multivalent functions

analytic functions bounded variation bounded boundary rotation strongly starlike functions


Dziok, Jacek. GENERALIZATIONS OF STRONGLY STARLIKE FUNCTIONS. Taiwanese J. Math. 18 (2014), no. 1, 39--51. doi:10.11650/tjm.18.2014.2986. https://projecteuclid.org/euclid.twjm/1499706330

Export citation


  • M. K. Aouf, Some inclusion relationships associated with Dziok Srivastava operator, Appl. Math. Comput., 216 (2010), 431-437.
  • S. Bhargava and R. S. Nanjunda, Convexity of a class of functions related to classes of starlike functions and functions with boundary rotation, Ann. Polon. Math., 49(3) (1989), 229-235.
  • N. E. Cho, O. S. Kwon and H. M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl., 292 (2004), 470-483.
  • H. B. Coonce and M. R. Ziegler, Functions with bounded Mocanu variation, Rev. Roumaine Math. Pures Appl., 19 (1974), 1093-1104.
  • J. Dziok, Applications of multivalent prestarlike functions, Appl. Math. Comput., 221 (2013), 230-238.
  • J. Dziok, Applications of the Jack lemma, Acta Math. Hungar., 105 (2004), 93-102.
  • J. Dziok, Characterizations of analytic functions associated with functions of bounded variation, Ann. Polon. Math., to appear.
  • J. Dziok, Classes of functions defined by certain differential-integral operators, J. Comput. Appl. Math., 105(1-2) (1999), 245-255.
  • J. Dziok, Inclusion relationships between classes of functions defined by subordination, Ann. Polon. Math., 100 (2011), 193-202.
  • J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14 (2003), 7-18.
  • P. J. Eenigenburg, S. S. Miller, P. T. Mocanu and O. M. Reade, Second order differential inequalities in the complex plane, J. Math. Anal. Appl., 65 (1978), 289-305.
  • J.-L. Liu and K. I. Noor, On subordinations for certain analytic functions associated with Noor integral operator, Appl. Math. Comput., 187 (2007), 1453-1460.
  • D. J. Hallenbeck and T. H. MacGregor, Linear Problems and Convexity Techniques in Geometric Function Theory, Pitman Advanced Publishing Program, Boston, Pitman, 1984.
  • E. J. Moulis, Generalizations of the Robertson functions, Pacific J. Math., 81 (1979), 167-174.
  • K. I. Noor and S. Hussain, On certain analytic functions associated with Ruscheweyh derivatives and bounded Mocanu variation, J. Math. Anal. Appl., 340(2) (2008), 1145-1152.
  • K. I. Noor and S. N. Malik, On generalized bounded Mocanu variation associated with conic domain, Math. Comput. Modelling, 55(3-4) (2012), 844-852.
  • K. I. Noor and A. Muhammad, On analytic functions with generalized bounded Mocanu variation, Appl. Math. Comput., 196(2) (2008), 802-811.
  • K. I. Noor and W. Ul-Haq, On some implication type results involving generalized bounded Mocanu variations, Comput. Math. Appl., 63(10) (2012), 1456-1461.
  • V. Paatero, Über die konforme Abbildung von Gebieten deren Ränder von beschränkter Drehung sind, Ann. Acad. Sei. Fenn. Ser A, 33 (1931), 1-79.
  • J. Patel, A. K. Mishra and H. M. Srivastava, Classes of multivalent analytic functions involving the Dziok-Srivastava operator, Comput. Math. Appl., 54 (2007), 599-616.
  • K. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math., 31 (1975), 311-323.
  • K. Piejko and J. Sokó\ptmrs \l, On the Dziok-Srivastava operator under multivalent analytic functions, Appl. Math. Comp., 177 (2006), 839-843.
  • B. Pinchuk, Functions with bounded boundary rotation, Isr. J. Math., 10 (1971), 7-16.
  • S. Ruscheweyh, Linear Operators Between Classes of Prestarlike Functions, Comm. Math. Helv., 52 (1977), 497-509.
  • H. M. Srivastava and A. Y. Lashin, Subordination properties of certain classes of multivalently analytic functions, Math. Comput. Modelling, 52 (2010), 596-602.
  • Z.-G. Wang, G.-W. Zhang and F.-H. Wen, Properties and characteristics of the Srivastava-Khairnar-More integral operator, Appl. Math. Comput., 218 (2012), 7747-7758.