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An additive functional inequality in matrix normed spaces. (English) Zbl 1285.39011

In this paper, the authors give some interesting results on the generalized Hyers-Ulam-Rassias stability of an additive functional inequality in matrix normed spaces. The authors use the direct method, following [P. Gǎvruţa, J. Math. Anal. Appl. 184, No. 3, 431–436 (1994; Zbl 0818.46043)] and the fixed point method, following [L. Cǎdariu and V. Radu, JIPAM, J. Inequal. Pure Appl. Math. 4, No. 1, Paper No. 4 (2003; Zbl 1043.39010)].

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
47L25 Operator spaces (= matricially normed spaces)
47H10 Fixed-point theorems
39B72 Systems of functional equations and inequalities
46L07 Operator spaces and completely bounded maps
39B52 Functional equations for functions with more general domains and/or ranges
39B62 Functional inequalities, including subadditivity, convexity, etc.
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