Sur l'approximation des solutions des équations à l'aide des suites à éléments dans un espaces de Banach: On the approximation of solutions of equations using sequences with elements in a Banach space - Păvăloiu, Ion (Anal. Numér. Théor. Approx., 1976)
Let \(X\) be a Banach space, \(Y\) a normed space \(P:X→ Y\) a nonlinear operator and the equation \(P\left( x\right) =0\) with solution \(x^{*}\). Consider \(Σ:=\left( x_{n}\right) _{n≥0}\) a sequence from \(X\) and define the convergence order of \(Σ\) with respect to the solution of equation \(P\left( x\right) =0\). We give a general result with sufficient conditions such that the sequence \(Σ\) converge to the solution \(x^{*}\) with a given convergence order.