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Minimax theorems without changeless proportion

Liang-Ju Chu, Chi-Nan Tsai (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The so-called minimax theorem means that if X and Y are two sets, and f and g are two real-valued functions defined on X×Y, then under some conditions the following inequality holds: i n f y Y s u p x X f ( x , y ) s u p x X i n f y Y g ( x , y ) . We will extend the two functions version of minimax theorems without the usual condition: f ≤ g. We replace it by a milder condition: s u p x X f ( x , y ) s u p x X g ( x , y ) , ∀y ∈ Y. However, we require some restrictions; such as, the functions f and g are jointly upward, and their upper sets are connected. On the other hand, by using some properties...

Multifunctions of two variables: examples and counterexamples

Jürgen Appell (1996)

Banach Center Publications

A brief account of the connections between Carathéodory multifunctions, Scorza-Dragoni multifunctions, product-measurable multifunctions, and superpositionally measurable multifunctions of two variables is given.

Multi-valued operators and fixed point theorems in Banach algebras

Bapur Chandra Dhage (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, two multi-valued versions of the well-known hybrid fixed point theorem of Dhage [6] in Banach algebras are proved. As an application, an existence theorem for a certain differential inclusion in Banach algebras is also proved under the mixed Lipschitz and compactness type conditions.

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