In this paper, we study the Chebyshev centres of bounded subsets of normed spaces and obtain a norm inequality for relative centres. In particular, we prove that if T is a remotal subset of an inner product space H, and F is a star-shaped set at a relative Chebyshev centre c of T with respect to F, then llx - qT (x)1I2 2 Ilx-cll2 + Ilc-qT (c) 112 x E F, where qT : F + T is any choice functi...

Couples reported on bases for giving support and on relationship satisfaction just prior to and approximately 2 years into marriage. Overall, a need-based, noncontingent (communal) norm was seen as ideal and was followed, and greater use of this norm was linked to higher relationship satisfaction. An exchange norm was seen as not ideal and was followed significantly less frequently than was a c...

The concept of Conditional Value-at-Risk (CVaR) is used in various applications in uncertain environment. This paper introduces CVaR (superquantile) norm for a random variable, which is by de nition CVaR of absolute value of this random variable. It is proved that CVaR norm is indeed a norm in the space of random variables. CVaR norm is de ned in two variations: scaled and non-scaled. L-1 and L...

we de ne approximate xed point in fuzzy norm spaces and prove the existence theorems, we also consider approximate pair constructive map- ping and show its relation with approximate fuzzy xed point.

This paper studies four families of polyhedral norms parametrized by a single parameter. The first two families consist of the CVaR norm (which is equivalent to the D-norm, or the largest-k norm) and its dual norm, while the second two families consist of the convex combination of the 1and ∞-norms, referred to as the deltoidal norm, and its dual norm. These families contain the 1and ∞-norms as ...