On Algebraic Properties of the Family of Weakly Świa̧tkowski Functions

Abstract In the paper we will focus on weakly Światkowski functions. We say that f satisfies weak Świa̧tkowski condition (or is a function) if for all $$x_1, x_2$$ x 1 , 2 with $$f(x_1)< f(x_2)$$ f ( ) < there point x between $$x_1$$ and $$x_2$$ such $$f(x_1)<f(x)< . This definition modification of condition, in which mentioned above has to be continuity examine some properties functions consider lineability algebrability families related them.