In this paper we give a characterization of pointwise and uniform convergence of sequences of homogeneous polynomials on a Banach space by means of the convergence of their level sets. Results are obtained both in the real and the complex cases, as well as some generalizations to the nonhomogeneous case and to holomorphic functions in the complex case. Kuratowski convergence of closed sets is u...

A general nonlinear framework for an Ishikawa-hybrid proximal point algorithm using the notion of A, η -accretive is developed. Convergence analysis for the algorithm of solving a nonlinear set-valued inclusions problem and existence analysis of solution for the nonlinear set-valued inclusions problem are explored along with some results on the resolvent operator corresponding to A, η -accretiv...

Abstract. This paper concerns the structure of the space C of real valued cocycles for a flow (X,Zm). We show that C is always larger than the set of cocycles cohomologous to the linear maps if the flow has a free dense orbit. By considering appropriate dual spaces for C, we obtain the concept of an invariant cocycle integral. The extreme points of the set of invariant cocycle integrals paralle...

We study two-layer neural networks whose domain and range are Banach spaces with separable preduals. In addition, we assume that the image space is equipped a partial order, i.e. it Riesz space. As nonlinearity choose lattice operation of taking positive part; in case $\mathbb R^d$-valued this corresponds to ReLU activation function. prove inverse direct approximation theorems Monte-Carlo rates...

The problem of ranking, in which the goal is to learn a real-valued ranking function that induces a ranking or ordering over an instance space, has recently gained much attention in machine learning. We study generalization properties of ranking algorithms using the notion of algorithmic stability; in particular, we derive generalization bounds for ranking algorithms that have good stability pr...

We provide a full large deviation principle (LDP) for the uniform measure on certain ensembles of convex lattice polygons. This LDP provides for the analysis of concentration of the measure on convex closed curves. In particular, convergence to a limiting shape results in some particular cases, including convergence to a circle when the ensemble is deened as those centered convex polygons, with...

The problem of ranking, in which the goal is to learn a real-valued ranking function that induces a ranking or ordering over an instance space, has recently gained attention in machine learning. We study generalization properties of ranking algorithms, in a particular setting of the ranking problem known as the bipartite ranking problem, using the notion of algorithmic stability. In particular,...

Abstract: In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over [0,1]. Some properties of GIVIFMs are studied using the definition of comparability of ...

Asymptotic expansions for U-statistics and V-statistics with degenerate kernels are investigated, respectively, the remainder term O(n1−p/2), some p≥4, is shown in both cases. From results, it obtained that asymptotic Crame´r–von Mises statistics of uniform distribution U(0,1) hold On1−p/2 any p≥4. The scheme proof based on three steps. first one almost sure convergence a Fourier series expansi...