If it is proved, where it is published?

Ostrowski has defined the efficiency index as EI = q^(1/p), where q is the order of convergence and p is the number of function evaluations for each iteration.

A. M. Ostrowski, “Solution of Equations and Systems of Equations”, Academic Press, second edition (1966).

On the other hand, Kung and Traub conjecture says that: q_opt = 2^(p – 1)

H. T. Kung and J. F. Traub, “Optimal order of one-point and multipoint iteration” Journal of

the ACM, vol. 21, no. 4, pp. 643–651, 1974.

https://doi.org/10.1145/321850.321860

Simple substitution shows that EI(p) = 2^(1-1/p). The limit of EI(p) for p -> ∞ is 2. Of course, in case we assume that Kung and Traub conjecture is true, which is not proven as far as I know.