In this paper, by using C-class functions, we will present a coupled …xed problem in b-metric space for the single-valued operators satisfying a generalized contraction condition. First part of the paper is related to some …xed point theorems, the second part presents the uniqueness and existence for the solution of the coupled …xed point problem and in the third part we...

We introduce topological definitions of expansivity, shadowing, and chain recurrence for homeomorphisms. They generalize the usual definitions for metric spaces. We prove various theorems about topologically Anosov homeomorphisms (maps that are expansive and have the shadowing property) on noncompact and non-metrizable spaces that generalize theorems for such homeomorphisms on compact metric sp...

We use the shadowing approach to study the long-time behavior of numerical approximations of semilinear parabolic equations. We show that the corresponding nonlinear semigroup has a Lipschitz shadowing property in a neighborhood of its global attractor. The proof is based on reduction to an inertial manifold and application of shadowing techniques developed for nite-dimensional systems. When ap...

Scaffolding and shadowing techniques have been shown to improve language learners’ reading comprehension. However, little attention has been paid to the comparative effectiveness of these techniques. This study investigated the effect of three selected scaffolding techniques (peer scaffolding, distributed scaffolding, and reciprocal scaffolding) versus three types of shadowing (complete shadowi...

We describe the limit sets in affine control systems, in affine differential systems with impulses. In contrast with the fixed points in ODE case, these sets may have a fractal structure. We give estimations of their Hausdorff dimension. For these systems we extend the notion of Shadowing Property and state this property in the neighborhoods of the attractors and repellers in control systems.

Inspired by a recent novel work of Good and Meddaugh, we establish fundamental connections between shadowing, finite order shifts, ultrametric complete spaces. We develop theory shifts type for infinite alphabets. call them order. the basic shadowing property in general metric spaces, exhibiting similarities differences with compact connect these two theories setting zero-dimensional showing th...

discrete iterated function systems discrete iterated function systems representation of discrete sequences with dimensional discrete iterated function systems discrete iterated function systems stochastic discrete scale invariance: renormalization representation of discrete sequences with high-dimensional power domains and iterated function systems fractal tilings from iterated function systems...

We study continuous maps of the unit interval into itself We determine necessary and su cient conditions so that all pseudo orbits can be approximated by orbits with the same initial point

We show that if a volume-preserving diffeomorphism belongs to the C1-interior of the set of all volume preserving diffeomorphisms having the periodic shadowing property then it is Anosov. Mathematics Subject Classification: 37C10, 37C50, 37D20