Browsing by Subject "extension theorem"

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Access status: Open Access ,
Extensions of solutions of a functional equation in two variables
(2009) Matkowski, Janusz
An extension theorem for the functional equation of several variables $f(M(x,y))=N(f(x),f(y)),$ where the given functions $M$ and $N$ are left-side autodistributive, is presented.
Access status: Open Access ,
On extension of solutions of a simultaneous system of iterative functional equations
(2009) Matkowski, Janusz
Some sufficient conditions which allow to extend every local solution of a simultaneous system of equations in a single variable of the form $\varphi(x) = h (x, \varphi[f_1(x)],\ldots,\varphi[f_m(x)]),$ $\varphi(x) = H (x, \varphi[F_1(x)],\ldots,\varphi[F_m(x)]),$ to a global one are presented. Extensions of solutions of functional equations, both in single and in several variables, play important role (cf. for instance [M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers, Warsaw, 1968, M. Kuczma, B. Choczewski, R. Ger, Iterative functional equations, Encyclopedia of Mathematics and Its Applications v. 32, Cambridge, 1990, J. Matkowski, <a href="https://repo.agh.edu.pl/handle/AGH/50094">Iteration groups, commuting functions and simultaneous systems of linear functional equations</a>, Opuscula Math. 28 (2008) 4, 531-541]).
Access status: Open Access ,
The equality case in some recent convexity inequalities
(2011) Maksa, Gyula; Páles, Zsolt
In this paper, we investigate a functional equation related to some recently introduced and investigated convexity type inequalities.