Openness results for uniform K-stability

Stability results of variational systems under linear openness

In this paper we present the notion of (U, V )-openness and (U, V )metric regularity for a set-valued map, proving their equivalence. By using different approaches we show the stability with respect to the sum of maps of the (U, V )-openness property, both in the setting of Banach spaces, and of metric spaces.

Some Stability Results for Picard Iterative Process in Uniform Space

The following concepts shall be required in the sequel: Definition 1.1 [5, 27]. A uniform space (X,Φ) is a nonempty set X equipped with a nonempty family Φ of subsets of X ×X satisfying the following properties: (i) if U is in Φ, then U contains the diagonal {(x, x) |x ∈ X}; (ii) if U is in Φ and V is a subset of X ×X which contains U, then V is in Φ; (iii) if U and V are in Φ, then U ∩ V is in...

Stability results for set solution of fuzzy integro-differential systems

Regularity Lemma for k-uniform hypergraphs

Szemerédi’s Regularity Lemma proved to be a very powerful tool in extremal graph theory with a large number of applications. Chung [Regularity lemmas for hypergraphs and quasi-randomness, Random Structures and Algorithms 2 (1991), 241–252], Frankl and Rödl [The uniformity lemma for hypergraphs, Graphs and Combinatorics 8 (1992), 309–312, Extremal problems on set systems, Random Structures and A...

Uniform Deviation Bounds for k-Means Clustering

Uniform deviation bounds limit the difference between a model’s expected loss and its loss on a random sample uniformly for all models in a learning problem. In this paper, we provide a novel framework to obtain uniform deviation bounds for unbounded loss functions. As a result, we obtain competitive uniform deviation bounds for k-Means clustering under weak assumptions on the underlying distri...