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Abstract Let \(a<c<b)\) real numbers, \((\mathbb{B},|\cdot|)\) a (real or complex) Banach space, \(H\in C([a,b]\times [a,c]\times\mathbb{B},\mathbb{B})\), \(K\in C([a,b]^{2}\times\mathbb{B},\mathbb{B})\),  \(g\in C([a,b]),\mathbb{B} ,A:C([a,c],\mathbb{B})\rightarrow…