Related papers: Cosmic Divergence, Weak Cosmic Convergence, and Fi…
The aim of this paper is to generalize some fixed point theorems in the class of convex contraction of order $m$ on a complete suprametric space. Then, we will prove that the class of convex contraction of order m is strong enough to…
We extend to $p$-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise $\alpha$-averaged mappings. Our main…
We study the non-perturbative renormalisation of quantum gravity in four dimensions. Taking care to disentangle physical degrees of freedom, we observe the topological nature of conformal fluctuations arising from the functional measure.…
A cosmological constant fits all current dark energy data, but requires two extreme fine tunings, both of which are currently explained by anthropic arguments. Here we discuss anti-anthropic solutions to one of these problems: the cosmic…
We discuss cosmological models for an eternal universe. Physical observables show no singularity from the infinite past to the infinite future. While the universe is evolving, there is no beginning and no end - the universe exists forever.…
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…
Among the suggested solutions to the cosmological constant problem, we find the idea of a dynamic vacuum, with an energy density decaying with the universe expansion. We investigate the possibility of a variation in the gravitational…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
We deal with a dynamical mechanism in which a large cosmological constant, as suggested by inflationary scenarios, decays due to expansion of the universe. This mechanism has its origin in the gravitational coupling of the vacuum density.…
While numerous extensions of Banach's fixed point theorem typically offer only sufficient conditions for the existence and uniqueness of a fixed point and the convergence of iterative sequences, this study introduces a generalization…
We consider a two-dimensional model of gravity with the cosmological constant as a dynamical variable. The effective cosmological constant is derived when the universe has no initial boundary. It turns out to be extremely small if the…
If the reported measurements of the time variation of the fine structure constant from observations of distant QSOs are correct, combined with the Oklo limit they would strongly constrain the class of the quintessence potential. If these…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of…
In an undulant universe, cosmic expansion is characterized by alternating periods of acceleration and deceleration. We examine cosmologies in which the dark-energy equation of state varies periodically with the number of e-foldings of the…
The notion of Fej\'er monotonicity is instrumental in unifying the convergence proofs of many iterative methods, such as the Krasnoselskii-Mann iteration, the proximal point method, the Douglas-Rachford splitting algorithm, and many others.…
The topic of fixed points in digital metric spaces has drawn yet more publications with assertions that are incorrect, incorrectly proven, trivial, or incoherently stated. We discuss publications with bad assertions concerning fixed points…
Spacetimes which have been considered counter-examples to strong cosmic censorship are revisited. We demonstrate the classical instability of the Cauchy horizon inside charged black holes embedded in de Sitter spacetime for all values of…
The weakly contractive metric type fixed point result in Berinde [Nonlinear Anal. Forum, 9 (2004), 45-53] is "almost" covered by the related altering metric one due to Khan et al [Bull. Austral. Math. Soc., 30 (1984), 1-9]. Further…
The Cosmological Principle states that the universe is both homogeneous and isotropic. This, alone, is not enough to specify the global geometry of the spacetime. If we were able to measure both the Hubble constant and the energy density we…