Three remarks on a question of Aczél

  title={Three remarks on a question of Acz{\'e}l},
  author={Orr Shalit},
  journal={Aequationes mathematicae},
  • Orr Shalit
  • Published 1 September 2010
  • Mathematics
  • Aequationes mathematicae
At ISFE 2009 J. Aczel asked for the monotonic solutions of a certain functional equation. We show that when a parameter appearing in the equation takes a certain value there is a unique monotonic solution, and when it takes other values there are infinitely many monotonic solutions. Further, we comment on continuous and continuously differentiable solutions.