Search results for "metric space"

A General Approach on Picard Operators

2021

In the chapter there are presented the recent investigations concerning the existence and the uniqueness of fixed points for the mappings in the setting of spaces which are not metric with different functions of measuring the distance and in consequence with the various convergence concepts. In this way we obtain the systematized knowledge of fixed point tools which are, in some situations, more convenient to apply than the known theorems with an underlying usual metric space. The appropriate illustrative examples are also presented.

Representation of Quasi-Measure by Henstock–Kurzweil Type Integral on a Compact-Zero Dimensional Metric Space

2009

Abstract A derivation basis is introduced in a compact zero-dimensional metric space 𝑋. A Henstock–Kurzweil type integral with respect to this basis is defined and used to represent the so-called quasi-measure on 𝑋.

Henstock type integral in compact zero-dimensional metric space and quasi-measures representations

2012

Properties of a Henstock type integral defined on a compact zero-dimensional metric space are studied. Theorems on integral representation of so-called quasi-measures, i.e., linear functionals on the space of “polynomials” defined on the space of the above mentioned type, are obtained.

Measuring the Spatial Dispersion of Evolutionary Search Processes: Application to Walksat

2002

In this paper, we propose a simple and efficient method for measuring the spatial dispersion of a set of points in a metric space. This method allows the quantifying of the population diversity in genetic algorithms. It can also be used to measure the spatial dispersion of any local search process during a specified time interval. We then use this method to study the way Walksat explores its search space, showing that the search for a solution often includes several stages of intensification and diversification.

Nonlinear contractions involving simulation functions in a metric space with a partial order

2015

Very recently, Khojasteh, Shukla and Radenovic [F. Khojasteh, S. Shukla, S. Radenovic, Filomat, 29 (2015), 1189-1194] introduced the notion of Z-contraction, that is, a nonlinear contraction involving a new class of mappings namely simulation functions. This kind of contractions generalizes the Banach contraction and unifies several known types of nonlinear contractions. In this paper, we consider a pair of nonlinear operators satisfying a nonlinear contraction involving a simulation function in a metric space endowed with a partial order. For this pair of operators, we establish coincidence and common fixed point results. As applications, several related results in fixed point theory in a …

Errata to: Exceptional Sets for Quasiconformal Mappings in General Metric Spaces

2010

Approximation of fixed points of multifunctions in partial metric spaces

2013

Recently, Reich and Zaslavski [S. Reich and A.J. Zaslavski, Convergence of Inexact Iterative Schemes for Nonexpansive Set-Valued Mappings, Fixed Point Theory Appl. 2010 (2010), Article ID 518243, 10pages] have studied a new inexact iterative scheme for fixed points ofcontractive multifunctions. In this paper, using the partial Hausdorffmetric introduced by Aydi et al., we prove an analogous to a resultof Reich and Zaslavski for contractive multifunctions in the setting ofpartial metric spaces. An example is given to illustrate our result. 

A PU-integral on an abstract metric space.

1997

Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings

1997

Abstract We study quasi-isometries between products of symmetric spaces and Euclidean buildings. The main results are that quasi-isometries preserve the product structure, and that in the irreducible higher rank case, quasi-isometries are at finite distance from homotheties.

Active Learning of Recursive Functions by Ultrametric Algorithms

2014

We study active learning of classes of recursive functions by asking value queries about the target function f, where f is from the target class. That is, the query is a natural number x, and the answer to the query is f(x). The complexity measure in this paper is the worst-case number of queries asked. We prove that for some classes of recursive functions ultrametric active learning algorithms can achieve the learning goal by asking significantly fewer queries than deterministic, probabilistic, and even nondeterministic active learning algorithms. This is the first ever example of a problem where ultrametric algorithms have advantages over nondeterministic algorithms.