Journal of Mathematical Sciences

, Volume 240, Issue 1, pp 21–33 | Cite as

Growth of Entire Functions of Bounded L-Index in a Direction

  • A. I. Bandura
  • O. B. Skaskiv

We solve the problem of estimation of growth for the maximum modulus of an entire function of bounded L -index in a direction. Some generalizations of the earlier one-dimensional results are obtained.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. I. Bandura and O. B. Skaskiv, “Entire functions of bounded L -index in a direction,” Mat. Studii, 27, No. 1, 30–52 (2007).MathSciNetzbMATHGoogle Scholar
  2. 2.
    H. Wittich, Neuere Untersuchungen Über Eindeutige Analytische Funktionen, Springer-Verlag, Berlin etc. (1968).Google Scholar
  3. 3.
    A. D., Kuzyk and M. N. Sheremeta, “Entire functions of bounded ℓ -distribution of values,” Mat. Zametki, 39, No. 1, 3–13 (1986); English translation: Math. Notes, Acad. Sci. USSR, 39, No. 1, 3–8 (1986).Google Scholar
  4. 4.
    G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis. Bd. II, Springer-Verlag, Berlin, etc. (1964).Google Scholar
  5. 5.
    T. O. Banakh and V. O. Kushnir, “On growth and distribution of zeros of analytic functions of bounded ℓ -index in arbitrary domains,” Mat. Studii, 14, No. 2, 165–170 (2000).MathSciNetzbMATHGoogle Scholar
  6. 6.
    A. I. Bandura and O. B. Skaskiv, “Open problems for entire functions of bounded index in direction,” Mat. Stud., 43, No. 1, 103–109 (2015).MathSciNetzbMATHGoogle Scholar
  7. 7.
    B. Lepson, “Differential equations of infinite order, hyper-Dirichlet series and entire functions of bounded index,” in: Entire Functions and Related Parts of Analysis, Proc. Symp. Pure Math., La Jolla, Calif. (1966), Providence, RI.: Amer. Math. Soc., Vol. XI (1968), pp. 298–307.Google Scholar
  8. 8.
    F. Nuray and R. F. Patterson, “Entire bivariate functions of exponential type,” Bull. Math. Sci., 5, No. 2, 171–177 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    F. Nuray and R. F. Patterson, “Multivalence of bivariate functions of bounded index,” Le Matematiche, 70, No. 2, 225–233 (2015).MathSciNetzbMATHGoogle Scholar
  10. 10.
    S. M. Shah, “Entire functions of bounded index,” Proc. Amer. Math. Soc., 19, No. 5, 1017–1022 (1968).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    M. Sheremeta, Analytic Functions of Bounded Index, VNTL Publishers, Lviv (1999), (Math. Studies: Monograph Ser., Vol. 6.).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. I. Bandura
    • 1
  • O. B. Skaskiv
    • 2
  1. 1.Ivano-Frankivs’k National Technical University of Oil and GasIvano-Frankivs’kUkraine
  2. 2.I. Franko Lviv National UniversityLvivUkraine

Personalised recommendations