Dual topology for the function space topologies multifunctions are introduced and investigated. It is found that a T on CM(Y,Z) splitting (resp. admissible) if only its dual pair (T+,T?) admissible). Similarly, T(T+,T?)

Using new properties of dual functions, we show that the method of constructing the dual bases recently presented in [P. Woźny, J. Comput. Appl. Math. 245 (2013), 75–85] can be significantly simplified. Next, we propose a simple algorithm of constructing the dual B-spline functions, which can be useful in solving some approximation problems related to numerical analysis or computer graphics.

In this paper, we review the role of self-duality in the theory of aggregation functions, the dual decomposition of aggregation functions into a self-dual core and an anti-self-dual remainder, and some applications to welfare, inequality, and poverty measures. © 2015 Elsevier B.V. All rights reserved.