Selecting families and their applications
Deguire and Lassonde [P. Deguire, M. Lassonde, Familles selectantes, Topol. Methods Nonlinear Anal. 5 (1995) 261-269] extend the concept of continuous selection and introduce the notion of selecting family for a family of set-valued mappings. In this paper, we first establish a new existence theorem of selecting families. The existence of the selecting families will be then used in order to obtain several fixed component theorems of Fan-Browder type, an intersection result, a maximal element theorem for a family of set-valued mappings and a minimax inequality.
A Minimax Inequality and its Applications to Fixed Point Theorems in R-trees
Recently, Kirk and Panyanak proved the KKM mapping principle in R-trees. In this paper, using this principle, we establish an R -tree version of famous Fan's minimax inequality and we apply this result to get some fixed point and best approximation theorems.
FURUTA INEQUALITY AND ITS RELATED TOPICS
This article is devoted to a brief survey of Furuta inequality and its related topics. It consists of 4 sections: 1. From Lowner-Heinz inequality to Furuta inequality, 2. Ando-Hiai inequality, 3. Grand Furuta inequality, and 4. Chaotic order.