Abstract. Inspired by the papers by Abbas, Aczél and by Chudziak and Tabor, we consider the problem of existence and uniqueness of extensions for the generalized Pexider equationwhere D is a nonempty open subset of a normed space. We show that the connectedness of D, assumed in the mentioned above papers, can be weakened.Mathematics Subject Classification. 39B52, 39B82.
Let (G, +) be a commutative group and S be its subsemigroup. We show that, under some natural assumptions on (G, +) and S, every solution of the Popoviciu type functional equation on S can be uniquely extended to the solution of the equation on G.
Willingness to pay WTP(X) for a lottery X , represented by a finitely-supported probability distribution on R , is the highest amount an individual is willing to pay for X . Willingness to accept WTA(X) is the smallest amount for which an individual would accept the sell of X . We deal with these notions under Rank-Dependent Utility, one of the behavioral models of decision making under risk. Applying some results concerning a comparison of quasideviation means, we characterize the properties of willingness to pay and willingness to accept related to the experimentally observed disparity between them.
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