Let $X,Y$ be the normed spaces, $C\subset X$ a convex set, and $T:C\rightarrow Y$ a continuous mapping. Some weak conditions implying the Lipschitz continuity of $T$ are presented. Applications to the fixed point theory and theory of composition operators are presented.
Banach J. Math. Anal.
1(2):
237-244
(2007).
DOI: 10.15352/bjma/1240336222