Solving Chisini’s functional equation
Copyright policy )Solving Chisini’s functional equation
We investigate the n-variable real functions G that are solutions of the Chisini functional equation F(x)=F(G(x),...,G(x)), where F is a given function of n real variables. We provide necessary and sufficient conditions on F for the existence and uniqueness of solutions. When F is nondecreasing in each variable, we show in a constructive way that if a solution exists then a nondecreasing and idempotent solution always exists. We also provide necessary and sufficient conditions on F for the existence of continuous solutions and we show how to construct such a solution. We finally discuss a few applications of these results.
- University of Luxembourg Luxembourg
idempotency, quasi-inverse function, level surface mean, 26E60, 39B12, 39B22 (Primary) 26B05, 26B35 (Secondary), Shepard's metric interpolation, Continuity and differentiation questions, quasi-idempotency, Functional Analysis (math.FA), Mathematics - Functional Analysis, Functional equations for real functions, Special properties of functions of several variables, Hölder conditions, etc., Chisini's functional equation, FOS: Mathematics, : Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Iteration theory, iterative and composite equations, : Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Chisini mean, Means
idempotency, quasi-inverse function, level surface mean, 26E60, 39B12, 39B22 (Primary) 26B05, 26B35 (Secondary), Shepard's metric interpolation, Continuity and differentiation questions, quasi-idempotency, Functional Analysis (math.FA), Mathematics - Functional Analysis, Functional equations for real functions, Special properties of functions of several variables, Hölder conditions, etc., Chisini's functional equation, FOS: Mathematics, : Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Iteration theory, iterative and composite equations, : Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Chisini mean, Means
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