Abstract
Our main result is that two point interpolatory subdivision schemes using C k nonlinear averaging rules on pairs of real numbers generate real-valued functions that are also C k . The significance of this result is the following consequence: Suppose that S is a subdivision algorithm operating on sequences of real numbers using linear binary averaging that generates C m real-valued functions and S ¯ is the same subdivision procedure where linear binary averaging is replaced everywhere in the algorithm by a C n nonlinear binary averaging rule on pairs of real numbers; then the functions generated by the nonlinear subdivision scheme S ¯ are C k , where k = min ( m , n ) .
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