A fixed point theorem for monotone functions Original Research Article

The main result of this work states that if View the MathML sourcef:R+m→R+m is increasing and continuous and the set S={x≥0:f(x)≤x}S={x≥0:f(x)≤x} is bounded and contains some x′>0x′>0 then there is a non-zero fixed point of ff, i.e. f(x)=x≠0f(x)=x≠0. If f:Rm→Rmf:Rm→Rm is increasing and continuous and the set {x:f(x)≤x}{x:f(x)≤x} is bounded and contains x″x″ and x′x′, x″