I realize Calculus is difficult enough without having to learn computer math notation.
However, please clarify your question,
L(f,p) is not a standard or universal notation. It could be a variation of Lipschitz condition in analysis. Alternately, the L(f,p) a notation meaning estimate the limit a x goes to zero using the x values x = 1, x = 1/2, x = 1/4, x =0. Your question could be asking something entirely different.