Lesche stability of k-entropy

The Lesche stability condition for the Shannon entropy (J. Stat. Phys. 27 (1982) 419), represents a fundamental test, for its experimental robustness, for systems obeying the Maxwell- Boltzmann statistical mechanics. Of course, this stability condition must be satisfied by any entropic functional candidate to generate non-conventional statistical mechanics. In the present effort we show that the k-entropy, recently introduced in literature (Phys. Rev. E 66 (2002) 056125), satisfies the Lesche stability condition.