Applications of Relations and Relators in the
Extensions of Stability Theorems for Homogeneous and Additive Functions
Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions
Institute of Mathematics, University of Debrecen,
H-4010 Debrecen, Pf. 12,
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 2-homogeneous 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.
the Convergence in Law of Iterates of Random-Valued Functions
On the Convergence in Law of Iterates of Random-Valued Functions
UniwersytetŚląski, Instytut Matematyki
Given a probability space (Ω, A, P) a separable and complete metric space X with the σ-algebra B of all its Borel subsets and a B A -measurable f : X * Ω → X we consider its iterates fn, n N, defined on X * ΩN by f1(x,ω) = f(x,ω1) and fn+1(x,ω)=f(fn(x,ω),ωn+1), provide a simple criterion for the convergence in law of fn(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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