A Tingley’s type problem in n-normed spaces

Huang, Xujian; Tan, Dongni

doi:10.1007/s00010-019-00637-w

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2023

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“…The above definitions, properties of m-normed spaces as well as information on some problems investigated in such spaces can be found, for example, in [3,5,16,21,23]. Now, we can formulate and prove our result on the stability of functional equation (3).…”

Section: Resultsmentioning

confidence: 96%

Stability of a General Functional Equation in m-Banach Spaces

Ciepliński

2023

Bull. Malays. Math. Sci. Soc.

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In this note, the Ulam stability of a general functional equation in several variables is investigated. It is shown that this equation is Ulam stable in m-Banach spaces. Since a particular case of the considered equation is, among others, a functional equation introduced by Ji et al. and Zhao et al. for a characterization of the so-called multi-quadratic mapping, a result on its stability is also presented. Moreover, some other applications are provided.

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