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## Main Question or Discussion Point

for which f: [tex]R[/tex] [tex]\rightarrow[/tex] [tex]R[/tex] such that

[tex]\forall[/tex] [tex]x,y[/tex][tex]\in[/tex] [tex]R[/tex]

does

| [tex]f(y)[/tex] - [tex]f(x)[/tex] | [tex]\mid[/tex] [tex]\leq[/tex] [tex](y-x)^2[/tex]

hold

[tex]\forall[/tex] [tex]x,y[/tex][tex]\in[/tex] [tex]R[/tex]

does

| [tex]f(y)[/tex] - [tex]f(x)[/tex] | [tex]\mid[/tex] [tex]\leq[/tex] [tex](y-x)^2[/tex]

hold