Let L1 be the set of all mappings f : Zp → Zp of the space of all p-adic integers Zp into itself that satisfy Lipschitz condition with a constant 1. We prove that the mapping f ∈L1 is ergodic with respect to the normalized Haar measure on Zp if and only if f induces a single cycle permutation on each residue ring Z/pZ modulo p, for all k = 1,2,3, . . .. The multivariate case, as well as measure...

We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G < Mod(S) satisfies certain conditions that imply G is quasi-isometrically embedded in Mod(S), then a purely pseudo-Anosov subgroup H < G is convex cocompact in Mod(S) if and only if it is combinatorially quasiconve...

We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure. The proof is based on solving a free boundary problem for a system of partial differential equations consisting of an elliptic equation and a transport equa...

In this paper, we investigate the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for a class of neural networks, the neutral system has mixed time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we drive a new criterion for the robust stability of a class of neural networks w...

Based on a notion of relatively maximal m -relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing Rockafellar’s theorem 1976 on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this newmodel, is simpler and compact than that of the celebrated technique of R...

In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on two well-known projection method and the hybrid (or outer approximation) method. However we do not use an extrapolation step in the projection method. The absence of one projection in our method is explained by sl...

In this paper we introduce an iterative process for finding a common element of the set of common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz continuous mapping. The iterative process is based on two known methods hybrid and extragradient. We obtain a strong convergence theorem for three seq...

Nonlinear functions, including nonlinear iterated function systems, have interesting fixed points. We present a non-Lipschitz theoretical approach to nonlinear function system fixed points which generalizes to non-contractive functions, compare several methods for evaluating such fixed points on modern graphics hardware, and present a nonlinear generalization of Barnsley’s Deterministic Iterati...

In the development of first-order methods for smooth (resp., composite) convex optimization problems, where functions with Lipschitz continuous gradients are minimized, gradient mapping) norm becomes a fundamental optimality measure. Under this measure, fixed iteration algorithm optimal complexity case is known, while determining number to obtain desired accuracy requires prior knowledge distan...

This article discusses Lipschitz properties of generated aggrega-tion functions. Such generated functions include triangular norms and conorms, quasi-arithmetic means, uninorms, nullnorms and continuous generated functions with a neutral element. The Lipschitz property guarantees stability of aggregation operations with respect to input inaccuracies, and is important for applications. We provid...