Special solutions of a general iterative functional equation
It is well known that functions satisfying formally functional equations need be neither continuous nor anywhere differentiable (in the Leibniz-Newton sense). It is, however, possible that, subject to sufficiently severe restrictions, particular solutions of functional equations may be locally similar to those of ordinary differential equations (ODEs). The existence and uniqueness theorems of this paper are established in such a framework, the key role being played by Banach's contraction principle. No concrete solution is constructed. In the introduction it is mentioned that functional equations are significant for the understanding of ``dynamical systems''. No justification is provided how time-derivatives (velocities, accelerations, induced fields, etc.) are taken into account, and how physical time enters into the considered functional equations. A reduction method is proposed for two particular functional series equations to the considered `general' form, but neither is solved. The references are limited to papers `advocating' a single ``school of thought''.
scientific article; zbMATH DE number 5126573