Local stability of mappings on multi-normed spaces

[摘要] First we investigate the Hyers–Ulam stability of the Cauchy functional equation for mappings from bounded (unbounded) intervals into Banach spaces. Then we study the Hyers–Ulam stability of the functional equation$f(xy)=xg(y)+h(x)y$ for mappings from bounded (unbounded) intervals into multi-normed spaces.

[学科分类] 航空航天科学

[关键词] Multi-normed space;Hyers–Ulam stability;Cauchy functional equation