113 research outputs found
On extension of solutions of a simultaneous system of iterative functional equations
Some sufficient conditions which allow to extend every local solution of a simultaneous system of equations in a single variable of the form 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, Iteration groups, commuting functions and simultaneous systems of linear functional equations, Opuscula Math. 28 (2008) 4, 531-541])
Iterations of mean-type mappings and invariant means
It is shown that, under some general conditions, the sequence of iterates
of every mean-type mapping on a finite dimensional cube converges to a unique
invariant mean-type mapping. Some properties of the invariant means and their applications
are presented
On a system of simultaneous iterative functional equations
A system of two simultaneous functional equations in a single
variable, related to a generalized Gołąb-Schinzel functional equation, is considered
A remark on periodic entire functions
Periodicity of an entire function is characterized by the behavior
of coefficients of its Maclaurin expansion
Explicit solutions of the invariance equation for means
Extending the notion of projective means we first generalize an invariance
identity related to the Carlson log given in a recent paper of P. Kahlig and J.
Matkowski, and then, more generally, given a bivariate symmetric, homogeneous
and monotone mean M, we give explicit formula for a rich family of pairs of
M-complementary means. We prove that this method cannot be extended for higher
dimension. Some examples are given and two open questions are proposed
On the commutation of generalized means on probability spaces
Let and be real-valued continuous injections defined on a non-empty
real interval , and let and be probability spaces in each of which there is at least one measurable
set whose measure is strictly between and .
We say that is a -switch if, for every -measurable function for
which is contained in a compact subset of , it holds where is the inverse of the corestriction of to , and
similarly for .
We prove that this notion is well-defined, by establishing that the above
functional equation is well-posed (the equation can be interpreted as a
permutation of generalized means and raised as a problem in the theory of
decision making under uncertainty), and show that is a -switch if and only if for some , .Comment: 9 pages, no figures. Fixed minor details. Final version to appear in
Indagationes Mathematica
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