Related papers: Fixed points, saddle points and universality

We introduce the concept of $\it{ startpoint}$ and $\it{endpoint}$ for multivalued maps defined on a quasi-pseudometric space. We investigate the relation between these new concepts and the existence of fixed points for these set valued…

In this paper, we establish some common fixed point results for a new class of pair of contractions mappings having functions as contractive parameters, and satisfying certain commutative properties.

The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point…

Model independent constraints on supersymmetric models emerge when certain couplings are drawn towards their infra-red (quasi) fixed points in the course of their renormalization group evolution. The general principles are first reviewed…

Deep neural networks trained with different architectures, objectives, and datasets have been reported to converge on similar visual representations. However, what remains unknown is which visual properties models actually converge on and…

Model uncertainty is a crucial issue in statistics, econometrics and machine learning, yet its definition remains ambiguous and is subject to various interpretations in the literature. So far, there has not been a universally accepted…

Machine learning (ML) is increasingly used in high-stakes settings, yet multiplicity - the existence of multiple good models - means that some predictions are essentially arbitrary. ML researchers and philosophers posit that multiplicity…

In this paper, we introduce a three-point analogue of \'Ciri\'c-Reich-Rus type mappings, termed as generalized \'Ciri\'c-Reich-Rus type mappings. We demonstrate that these mappings generally exhibit discontinuity within their domain of…

We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…

It has been argued that the only mathematically precise quantum descriptions of gravitating systems are from vantage points which allow an unbounded amount of information to be gathered. For an eternally inflating universe that means a hat,…

In this paper, we study some new common fixed point results of generalized contractive non-self multi-valued mappings on complete metric space.

Model sets are always Meyer sets, but not vice-versa. This article is about characterizing model sets (general and regular) amongst the Meyer sets in terms of two associated dynamical systems. These two dynamical systems describe two very…

Our purpose of this paper is to focus on fixed point property in fuzzy metric space. To achieve our objective, we will introduce a new contraction condition to examine the fixed point for multi-valued mapping, then we will be investigating…

In this work, we prove the existence of solutions for a tripled system of integral equations using some new results of fixed point theory associated with measure of noncompactness. These results extend some previous works in the literature,…

The aim of this paper is to present some fixed point theorems for generalized contractions by altering distance functions in a complete cone metric spaces endowed with a partial order. We also generalize fixed point theorems of J. Harjani,…

A common measure of a function's complexity is the count of its stationary points. For complicated functions, this count grows exponentially with the volume and dimension of their domain. In practice, the count is averaged over a class of…

Cosmological models that are locally consistent with general relativity and the standard model in which an object transported around the universe undergoes P, C and CP transformations, are constructed. This leads to generalization of the…

In this paper, we consider some equilibrium problems (or saddle point problems), in which the domains of the considered mappings are limited at some regions. These restricted regions are defined by some mappings which are called the…

The class of O-metric spaces generalize several existing metric-types in literature including metric spaces, b-metric spaces, and ultra metric spaces. In this paper, we discuss the properties of the topology induced by an O-metric and…

Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…