Unique solutions to power-transformed affine systems

Systems of the form x = (Axs)1/s + b arise in a range of economic and financial applications, where A is a linear operator acting on a space of real-valued functions (or vectors) and s is a nonzero real value. In these applications, attention is focused on positive solutions. We provide a simple characterization of existence and uniqueness of positive solutions when b is positive and A is irreducible. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.