Hyers-Ulam stability of substitution vector-valued integral operator

Zahra Moayyerizadeh
2018 Filomat  
For a substitution vector-valued integral operator T ϕ u , we determine necessary and sufficient conditions to have Hyers-Ulam stability using conditional expectation operators. Then, we present an example to illustrate our result. Definition 1.1 ([9] ). Let X, Y be normed linear spaces and T be a (not necessarily linear) mapping from X into Y . We say that T has the Hyers-Ulam stability if there exists a constant M > 0 with the following property: For any ∈ T(X), > 0 and f ∈ T(X) satisfying T
more » ... T(X) satisfying T f − ≤ , we can find f 0 ∈ T(X) such that T f 0 = and f − f 0 ≤ M . We call M a HUS constant for T, and denote the infimum of all HUS constants for T by M T . We refer the reader for the Hyers-Ulam stability of substitution operators on function spaces to [4, 9, 13, 14] and the
doi:10.2298/fil1818487m fatcat:ubter6jk2vad3klxfteucz5z7e