Continuous solutions of an iterative functional inequality on compact interval. (English) Zbl 0990.39025
Summary: A functional inequality that requires the convex combination of the iterates of an unknown function to be less than or equal to a given function on a compact interval is considered. An existence criterion for its continuous solutions is given which makes use of the existence of those of its associated functional equation.
MSC:
39B62 | Functional inequalities, including subadditivity, convexity, etc. |
39B12 | Iteration theory, iterative and composite equations |