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Journal: Annales Mathematicae Silesianae

On the structure of two-person, finite, zero-sum games

Zdzisław Wyderka

Language: EN | Published: 30-01-1990 | Abstract | pp. 127-131

The algebraical and topological structure of the set S? (resp. ????₁) of all n×m matrix games with saddle points (resp. with unique saddle point) in the space R^n×m of all such games is studied. It has been shown that ???? is a closed cone with vertex zero and includes the origin. Moreover, it is neither convex nor dense subset of R^n×m. The set ????₁ is a non-convex cone which does not include the origin. It is neither closed nor open.
The concept of “reserve of non-saddlexity” has been also introduced.

1990-01-30



Journal: Annales Mathematicae Silesianae

Jensen convex functions bounded above on nonzero Christensen measurable sets

Eliza Jabłońska

Language: EN | Published: 30-09-2009 | Abstract | pp. 53-55

We prove that every Jensen convex function mapping a real linear Polish space into ℝ bounded above on a nonzero Christensen measurable set is convex.

2009-09-30



Journal: Annales Mathematicae Silesianae

Hull-concave set-valued functions

Antonella Fiacca , Kazimierz Nikodem , Francesca Papalini

Language: EN | Published: 30-09-1994 | Abstract | pp. 211-216

A set-valued function F is called hull-concave if
F(tx + (1-t)y) ⊂ co(tF(x) + (1-t)F(y))
for all x,y from the domain of F and all t∈[0,1]. It is shown that if a hull-concave set-valued function F is defined on an open convex subset D of ℝⁿ and for every x∈D the set clF(x) is convex and bounded, then F is continuous on D. Some other properties of hull-concave set-valued functions are also given.

1994-09-30



Journal: Annales Mathematicae Silesianae

Stability of a system of generalized trigonometric equations

Irena Fidytek

Language: EN | Published: 29-09-1995 | Abstract | pp. 81-100

Addition formulas for generalized trigonometric functions corresponding to a given symmetric bounded and convex planar set containing the origin as an inner point are derived. Connections with the theory of characters on (semi) groups are considered. Hyers-Ulam stability of a suitable system of functional equations is investigated. It is also shown that superstability phenomenon fails to hold for that system.

1995-09-29