Geodesic
On Nearly Subadditive Maps
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 93-96.

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Several results on stability in spirit of Ulam and Hyers are obtained for classes of maps from groups to lattices satisfying the subadditivity condition $$ F(gh) \subset F(g)\cup F(h) \quad \text{for all }\ g,h \in G. $$
Keywords: subadditive set-valued maps on groups, addition theorems, stability problems. 
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E. V. Shul'man. On Nearly Subadditive Maps. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 93-96. http://geodesic.mathdoc.fr/item/FAA_2016_50_1_a10/

[1] D. H. Hyers, Proc. Nat. Acad. Sci. USA, 27 (1941), 222–224 | DOI | MR

[2] D. H. Hyers, G. Isac, T. M. Rassias, Stability of Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and their Applications, 34, Birkhauser, Boston, MA, 1998 | MR | Zbl

[3] E. Shulman, J. Funct. Anal., 263:5 (2012), 1468–1484 | DOI | MR | Zbl