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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 ( ). 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 Tdoi:10.2298/fil1818487m fatcat:ubter6jk2vad3klxfteucz5z7e