Fixed point of polynomial type nonlinear operators
A concept of generalized polynomial operators is considered, and a fixed-point problem with these operators is posed. The existence of a fixed point, with a minimum norm property, is stated and a power series representation is obtained. Problems of this kind appear, for instance, in some two-point boundary-value problems in optimal control.
Key WordsPolynomial operators nonlinear equations fixed points contraction mapping principle successive approximation
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