Related papers: Borwein-Preiss Variational Principle Revisited

This article extends to the vector setting the results of our previous work Kruger et al. (2015) which refined and slightly strengthened the metric space version of the Borwein-Preiss variational principle due to Li and Shi, J. Math. Anal.…

In this paper, we extend the Banach contraction principle to metric-like as well as partial metric spaces (not essentially complete) equipped with an arbitrary binary relation. Thereafter, we derive some fixed point results which are…

In this paper we prove the Stein-Weiss inequality in variable exponent Morrey spaces over a bounded domain. Our work extends earlier results in the variable exponent Lebesgue and Morrey settings, and utilizes new proof techniques applicable…

We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a…

A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…

We introduce and study spaces of multivariate functions of bounded variation generalizing the classical Jordan and Wiener spaces. Multivariate generalizations of the Jordan space were given by several prominent researchers but each of them…

The main aim of this note is to point out by means of counter-examples that some arguments of the proofs of two theorems about a "half variational principle" for multivalued maps, formulated recently by Vivas and Sirvent [Metric entropy for…

A refinement of Zhong's variational principle [Nonlin. Anal., 29 (1997), 1421-1431] is given, in the realm of almost metric structures. Applications to equilibrium points are also provided.

Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…

The objective of this work is the construction of `Boyd-Wong fixed point theorem' in the setting of generalized parametric metric space and discussion its application on existence criteria of solutions to a second order initial value…

Let $\pi:X\to Y$ be a factor map, where $(X,T)$ and $(Y,S)$ are topological dynamical systems. Let ${\bf a}=(a_1,a_2)\in {\Bbb R}^2$ with $a_1>0$ and $a_2\geq 0$, and $f\in C(X)$. The ${\bf a}$-weighted topological pressure of $f$, denoted…

We give a revised version of Schmidt's treatment of forms in many variables, which allows us to prove a Hasse principle under more lenient conditions on the number of variables than what had previously been thought possible with these…

We study variational principles for metric mean dimension. First we prove that in the variational principle of Lindenstrauss and Tsukamoto it suffices to take supremum over ergodic measures. Second we derive a variational principle for…

The support of minimizing measures of the causal variational principle on the sphere is analyzed. It is proven that in the case $\tau>\sqrt{3}$, the support of every minimizing measure is contained in a finite number of real analytic curves…

We prove in this article that every Borelian measure, for example, the distribution of a random variable, in separable Banach space has a support which is compact embedded Banach subspace; and prove that if the norm of the random variable…

As a result of some mistakes discovered in the paper mentioned in the title, Corollaries 3.5 and 3.17a) are withdrawn and a new proof is provided for Proposition 3.14, under the added assumption that the second dual of the underlying Banach…

We extend the parametric geometry of numbers (initiated by Schmidt and Summerer, and deepened by Roy) to Diophantine approximation for systems of $m$ linear forms in $n$ variables, and establish a new connection to the metric theory via a…

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…

We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals…

We consider Borwein-Preiss and Ekeland variational principles using distance functions that neither is symmetric nor enjoy the triangular inequality. All the given results rely exclusively on the convergence and continuity behaviors induced…