A note on two fixed point problems

We extend the applicability of the Exterior Ellipsoid Algorithm for approximating n-dimensional fixed points of directionally nonexpanding functions. Such functions model many practical problems that cannot be formulated in the smaller class of globally nonexpanding functions. The upper bound 2n2ln(2/ɛ) on the number of function evaluations for finding ɛ-residual approximations to the fixed points remains the same for the larger class. We also present a modified version of a hybrid bisection-secant method for efficient approximation of univariate fixed point problems in combustion chemistry.