In this paper we introduce the concept of bounded variation for functions defined on compact subsets of the complex plane , based on the notion of variation along a curve as defined by Ashton and Doust; We describe in detail the space so generated and show that it can be equipped, in a natural way, with the structure of a Banach algebra. We also present a necessary condition for a composition operator to act between two such spaces.
In this paper we present a necessary condition for an autonomous superposition operator to act in the space of functions of Waterman-Shiba bounded variation. We also show that if a (general) superposition operator applies such space into itself and it is uniformly bounded, then its generating function satisfies a weak Matkowski condition.
In this paper we present the concept of bounded second variation of a real valued function defined on a rectangle in . We use Hardy-Vitali type technics in the plane in order to extend the classical notion of function of bounded second variation on intervals of . We introduce the class , of all functions of bounded second variation on a rectangle , and show that this class can be equipped with a norm with respect to which it is a Banach space. Finally, we present two results that show that integrals...
Two games are inseparable by semivalues if both games obtain the same allocation whatever semivalue is considered. The problem of separability by semivalues reduces to separability from the null game. For four or more players, the vector subspace of games inseparable from the null game by semivalues contains games different to zero-game. Now, for five or more players, the consideration of a priori coalition blocks in the player set allows us to reduce in a significant way the dimension of the vector subspace...
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