On local characterization of the strong Światkowski property for a function f:[a,b]→ℝ.

Abstract

In this paper we introduce the idea of a function having the strong \'Swi\c{a}tkowski property at a point. The main result of this work is proving that the class of functions which have the %``locally" strong \'Swi\c{a}tkowski property at each point, is equal to the class of all strong \'Swi\c{a}tkowski functions.