Editing Equicontinuity (section)

=== Examples ===

*A set of functions with a common [[Lipschitz constant]] is (uniformly) equicontinuous. In particular, this is the case if the set consists of functions with derivatives bounded by the same constant.
*[[Uniform boundedness principle]] gives a sufficient condition for a set of continuous linear operators to be equicontinuous.
*A family of iterates of an [[analytic function]]  is  equicontinuous on the  [[Fatou set]].<ref>Alan F. Beardon, S. Axler, F.W. Gehring, K.A. Ribet : Iteration of Rational Functions: Complex Analytic Dynamical Systems. Springer, 2000; {{ISBN|0-387-95151-2}}, {{ISBN|978-0-387-95151-5}}; page 49</ref><ref>Joseph H. Silverman : The arithmetic of dynamical systems. Springer, 2007. {{ISBN|0-387-69903-1}}, {{ISBN|978-0-387-69903-5}}; page 22</ref>