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We develop a general framework for using duality to "transfer" stability results for a functional inequality to its dual inequality. As an application, we prove a stability bound for the Hardy-Littlewood-Sobolev inequality, which is related…
In this paper, we study some new common fixed point results of generalized contractive non-self multi-valued mappings on complete metric space.
In this paper, we study maximal subextension of $m$-subharmonic functions with given boundary values. We also prove stability on $m$-capacity of maximal subextension of $m$-subharmonic functions with given boundary values.
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
Using sheaf theory, I introduce a continuous theory of persistence for mappings between compact manifolds. In the case both manifolds are orientable, the theory holds for integer coefficients. The sheaf introduced here is stable to…
This paper is dedicated to the study of the stability of multiplicities of group representations.
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
In this paper, we present several necessary and sufficient conditions for a harmonic mapping to be normal. Also, we discuss maximum principle and five-point theorem for normal harmonic mappings. Furthermore, we investigate the convergence…
The existence, uniqueness, and exponential stability results for mild solutions to the fractional neutral stochastic differential system are presented in this article. To demonstrate the results, the concept of bounded integral contractors…
We prove that the upper bounds for the consistency strength of certain instances of mutual stationarity considered by Liu-Shelah~\cite{MR1469093} are close to optimal. We also consider some related and, as it turns out, stronger properties.
In this paper, some results on the existence of n-tuplet fixed points for multi-valued contraction mappings are proved via measure of noncompactness. As an application, the existence of solutions for a system of integral inclusions is…
In this paper we investigate the mean square asymptotic stability of a perturbed scalar linear stochastic functional differential equation. Specifically, we are able to give necessary and sufficient conditions on the forcing terms for…
We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…
The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of $\mathbb{R}$-valued functions, the result was later cast in a…
We study the weak $K_s$-saturation number of the Erd\H{o}s--R\'{e}nyi random graph $\mathbbmsl{G}(n, p)$, denoted by $\mathrm{wsat}(\mathbbmsl{G}(n, p), K_s)$, where $K_s$ is the complete graph on $s$ vertices. Kor\'{a}ndi and Sudakov in…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…
Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic,…