We introduce a new subclass of meromorphic Bazilevič-type functions defined with the help of a differential operator. We study some interesting properties of functions from this class, such as the arc length, the growth of coefficients, and the integral representations of functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. M. Ali and V. Ravichandran, “Classes of meromorphic alpha-convex functions,” J. Taiwan. Math., 14, 1479–1490 (2010).
F. M. Al-Oboudi and H. A. Al-Zakeri, “Applications of Briot–Bouquet differential subordination to certain classes of meromorphic functions,” J. Arab Math. Sci., 12, 1–14 (2005).
I. E. Bazilevič, “On a class of integrability in quadratures of a Loewner–Kufarev equation,” Math. Sb., 37, 471–476 (1955).
J. Dziok, “Meromorphic functions with bounded boundary rotation,” Acta Math. Sci., 34, 466–472 (2014).
G. M. Golusin, Geometrische Funktionentheorie, Berlin (1957).
A. W. Goodman, Univalent Functions, Polygonal Publ. House, Washington, New Jersey (1983).
S. A. Halim, S. G. Hamidi, and V. Ravichandran, “Coefficient estimates for meromorphic biunivalent functions,” Compt. Rend., Math., 351, 349–352 (2013).
D. J. Hallenbeck and T. H. MacGregor, Linear Problems and Convexity Techniques in Geometric Function Theory, Pitman, Boston (1984).
W. K. Hayman, “On functions with positive real part,” J. London Math. Soc., 36, 34–48 (1961).
W. Janowski, “Some extremal problem for certain families of analytic functions. I,” Ann. Polon. Math., 28, 298–326 (1973).
R. I. Libera and M. S. Robertson, “Meromorphic close-to-convex functions,” Michigan Math. J., 8, 167–175 (1961).
J. Noonan, “Meromorphic functions of bounded boundary rotation,” Michigan Math. J., 18, 343–352 (1971).
K. I. Noor, “On generalizations of close-to-convexity,” Mathematica, 23, 217–219 (1981).
K. I. Noor and K. Yousaf, “On classes of analytic functions related with generalized Janowski functions,” World Appl. Sci. J., 13, 40–47 (2011).
J. Pfaltzgraff and B. Pinchuk, “A variational method for classes of meromorphic functions,” J. Anal. Math., 24, 101–150 (1971).
C. Pommerenke, “On meromorphic starlike functions,” Pacif. J. Math., 13, 221–235 (1963).
C. Pommerenke, “On the coefficients of close-to-convex functions,” Michigan Math. J., 9, 259–269 (1962).
M. Raza and K. I. Noor, “A class of Bazilevič type functions defined by convolution operator,” J. Math. Inequal., 5, 253–261 (2011).
R. Singh, “On Bazilevič functions,” Proc. Amer. Math. Soc., 38, 261–271 (1973).
D. K. Thomas, “On Bazilevič functions,” Trans. Amer. Math. Soc., 132, 353–361 (1968).
D. K. Thomas, “On the coefficients of meromorphic univalent functions,” Proc. Amer. Math. Soc., 47, 161–166 (1975).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 10, pp. 1389–1404, October, 2019.
Rights and permissions
About this article
Cite this article
Noor, K.I., Ahmad, Q.Z., Orhan, H. et al. A Class of Meromorphic Bazilevič-Type Functions Defined by a Differential Operator. Ukr Math J 71, 1590–1607 (2020). https://doi.org/10.1007/s11253-020-01733-w
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-020-01733-w