The Fixed Point Iteration of Positive Concave Mappings Converges Geometrically if a Fixed Point Exists: Implications to Wireless Systems

We prove that the fixed point iteration of arbitrary positive concave mappings with nonempty set converges geometrically for any starting point. also show positivity is crucial this result to hold, and concept (nonlinear) spectral radius asymptotic provides us information about convergence factor. As a practical implication results shown here, we rigorously explain why some power control load estimation algorithms in wireless networks, which are particular instances iteration, have geometric simulations. These been typically derived by considering iterations general class standard interference mappings, so possibility sublinear rate could not be ruled out previous studies, except special cases often more restrictive than those considered here.