Construction of continuous solutions and stability for the polynomial-like iterative equation

Abstract Most of known results such as existence, uniqueness and stability for polynomial-like iterative equations were given under the assumption that the coefficient of the first order iteration term does not vanish. The existence with a non-zero leading coefficient was therefore raised as an open problem. It was positively answered for local C 1 solutions later. In this paper this problem is answered further by constructing C 0 solutions. Moreover, we discuss the stability of those C 0 solutions, which consequently implies a result of the stability for iterative roots.

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