A generalization of the proximate order

Doklady Bashkirskogo Universiteta. 2020. Volume 5. No. 1. pp. 1-6.


Khabibullin B. N.*
Bashkir State University
32 Zaki Validi Street, 450076 Ufa, Republic of Bashkortostan, Russia


The concept of proximate order is widely used in the theories of entire, meromorphic, subharmonic and plurisubharmonic functions. We give a general interpretation of this concept as a proximate growth function relative to a model growth function. If a function V is the proximate growth function with respect to the identity function on the positive semi-axis, then the function ln V is the classical proximate order. Our definition uses only one condition. This form of definition is also new for the classical proximate order.


  • growth function
  • proximate order
  • convex function
  • entire function
  • subharmonic function