Improved convergence results for the Nelder-Mead simplex method in low dimensional spaces

We prove two results on the convergence of the Nelder-Mead simplex method. Both theorems prove the convergence of the simplex vertices to a common limit point. The first result is an improved variant of the convergence theorems of [7] and [8], while the second one proves the convergence with probability 1.

Behavior of entanglement entropy near periodic orbits in a hamiltonian dynamical system

Entanglement entropy growth is studied under a form of dynamics that is based on iteration. This approach allows the investigation of the role of decoherence in producing increases of entropy. This has important consequences as far as the study of decoherence is concerned. It is indicated that results are generally independent of Hilbert space partitioning. It is seen that a deep relationship between classical dynamical entropy and the growth of entanglement entropy exists in this kind of model. The former acts to bound the latter and in the asymptotic region, they tend to a common limit.

Some Theorems on Integral and Rational Type Contractive Conditions in Dislocated Metric Space

In this article, we establish some coincidence points and common fixed point results on integral and rational type contractive conditions using E.A. and common limit range (CLR) properties in dislocated metric space.

Common Fixed Point Theorems for Six Self Maps in FM-Spaces Using Common Limit in Range Concerning Two Pairs of Products of Two Different Self-maps

In this article, we do a study of common fixed point theorems for six self-maps in FM-Spaces using common limit in range property concerning two pairs of products of two different self-maps. We use the properties (CLRTH) and (CLRSR) along with contractive type implicit relations to prove our results. In support of our result, an example has been provided. Our findings are like those of Kumar and Chouhan [12]. Kumar and Chauhan demonstrated their primary result in [12] by improving and generalizing Aalam, Kumar, and Pants' [1] results. In past, many authors have done study of common fixed point using (E-A) property (like Aalam et. al. [1] proved results using this property), and then these results were improved and generalized by using common (E-A) property as this property is superior to (E-A) property, as the closeness of subspace is required to prove a required result on common fixed point by using these properties, which is a drawback. We improve and generalize all results on these properties using common limit in range property. The goal of this note is to refine and generalize Kumar and Chauhan's [12] results on a common fixed point, as well as some earlier comparable results.

Expansion Mapping Theorem for Four Mappings Satisfying Common Limit in the Range Property in b-Metric Space

In the present paper, for four weakly compatible mappings in pairs, an expansion mapping theorem has been developed in b-metric space, meeting common limit range property. We proved this theorem without using the b-metric space's completeness condition. The result is an extension and generalization of several metric space results available. To confirm the finding, a suitable example is also discussed.

Extracontractual Liability Law as a Policy Instrument: Public Law in Disguise or in Chains?

Extracontractual liability law is no exception to the general trend of instrumentalisation of private law. It is increasingly being used to pursue goals other than its primary aim of compensation. This instrumentalisation is a dual phenomenon that has developed both out of top-down and bottom-up impulses. Although specific questions may arise for each of these two movements, they encounter a common limit. On a fundamental level, the instrumentalisation is restricted by extracontractual liability law’s primary compensatory function. Other functions, such as enforcement (of rights) or prevention, are grafted onto this primary function and can only be pursued to the extent that they are compatible with it. It relates to the tension created by pursuing public goals through extracontractual liability law as an essentially private law instrument. Attention is needed not to overstretch extracontractual liability law’s prerequisites, which are coherent with its private law embedding. It would turn extracontractual liability law into a dangerous passe-partout. Besides stretching the existing prerequisites, one may also consider alternative instruments for pursuing non-compensatory goals, such as preventive actions. Given the ubiquitous occurrence of the phenomenon, the present contribution will start from Belgian and Dutch law, although the conclusions may reach beyond these legal systems.

Coupled Fixed Point Theorems Employing CLR-Property on V -Fuzzy Metric Spaces

The introduction of the common limit range property on V -fuzzy metric spaces is the foremost aim of this paper. Furthermore, significant results for coupled maps are proven by employing this property on V -fuzzy metric spaces. More precisely, we introduce the notion of C L R Ω -property for the mappings Θ : M × M → M and Ω : M → M . We utilize our new notion to present and prove our new fixed point results.