Connections between the solutions of inequality systems and minimax assertions have been investigated in the past in many papers. In the present paper, we consider connections between the equivalence of two inequality systems depending on each other on the one hand and the validity of minimax results on the other hand. The inequality systems and the classical minimax relation are formulated by means of a function f:X×Y→E, where for X and Y no linear structure is supposed and E is an order-complete topological Riesz space with the order cone C. For E=R corresponding results can be found in papers by K. Fan . The present paper gives generalizations of results of Fan having relevance for vector optimization.
Inequality systems and minimax results without linear structure
MARTELLOTTI, Anna;SALVADORI, Anna
1990
Abstract
Connections between the solutions of inequality systems and minimax assertions have been investigated in the past in many papers. In the present paper, we consider connections between the equivalence of two inequality systems depending on each other on the one hand and the validity of minimax results on the other hand. The inequality systems and the classical minimax relation are formulated by means of a function f:X×Y→E, where for X and Y no linear structure is supposed and E is an order-complete topological Riesz space with the order cone C. For E=R corresponding results can be found in papers by K. Fan . The present paper gives generalizations of results of Fan having relevance for vector optimization.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
