


Paper's Title:
Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions
Author(s):
Árpád Száz
Institute of Mathematics, University of Debrecen,
H4010 Debrecen,
Pf. 12,
Hungary
szaz@math.klte.hu
Abstract:
By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.
Paper's Title:
On the Convergence in Law of Iterates of RandomValued Functions
Author(s):
Karol Baron
Uniwersytet
Śląski,
Instytut Matematyki
Bankowa 14,
PL40007 Katowice,
Poland
baron@us.edu.pl
Abstract:
Given a probability space (Ω, A, P) a separable and complete metric space X with the σalgebra B of all its Borel subsets and a B A measurable f : X * Ω → X we consider its iterates f^{n}, n N, defined on X * Ω^{N} by f^{1}(x,ω) = f(x,ω_{1}) and f^{n+1}(x,ω)=f(f^{n}(x,ω),ω_{n+1}), provide a simple criterion for the convergence in law of f^{n}(x,·))_{ n N}, to a random variable independent of x X , and apply this criterion to linear functional equations in a single variable.
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