In the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive resul...

Let $\overrightarrow{G}$ be a directed graph with no component of orderless than~$3$, and let $\Gamma$ finite Abelian group such that $|\Gamma|\geq 4|V(\overrightarrow{G})|$ or if $|V(\overrightarrow{G})|$ is large enough respect to an arbitrarily fixed $\varepsilon>0$ then (1+\varepsilon)|V(\overrightarrow{G})|$. We show there exists injective mapping $\varphi$ from $V(\overrightarrow{G})$ the...

OBJECTIVES The aim of this study was to analyze different anatomic mapping approaches for successful ablation of outflow tract tachycardia with R/S transition in lead V(3). BACKGROUND Idiopathic ventricular tachycardia can originate from different areas in the outflow tract, including the right and left ventricular endocardium, the epicardium, the pulmonary artery, and the aortic sinus of Val...

We propose and analyze the convergence of a novel stochastic algorithm for monotone inclusions that are sum of a maximal monotone operator and a single-valued cocoercive operator. The algorithm we propose is a natural stochastic extension of the classical forward-backward method. We provide a non-asymptotic error analysis in expectation for the strongly monotone case, as L. Rosasco DIBRIS, Univ...

* Correspondence: [email protected] Department of Mathematics, Sichuan University of Science and Engineering, Zigong, 643000, Sichuan, People’s Republic of China Full list of author information is available at the end of the article Abstract In this paper, we develop a new perturbed iterative algorithm framework with errors based on the variational graphical convergence of operator sequences w...

A list-assignment L to the vertices of G is an assignment of a set L(v) of colors to vertex v for every v ∈ V (G). An (L, d)-coloring is a mapping φ that assigns a color φ(v) ∈ L(v) to each vertex v ∈ V (G) such that at most d neighbors of v receive color φ(v). A graph is called (k, d)-choosable, if G admits an (L, d)-coloring for every list assignment L with |L(v)| ≥ k for all v ∈ V (G). In th...

We consider shape optimization problems governed by the unsteady Navier-Stokes equations by applying the method of mappings, where the problem is transformed to a reference domain Ωref and the physical domain is given by Ω = τ(Ωref) with a domain transformation τ ∈ W (Ωref). We show the Fréchet-differentiability of τ 7→ (v, p)(τ) in a neighborhood of τ = id under as low regularity requirements ...

This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems cocoercive equations. From point view, we compare convergence rates gradient descent, forward-backward, Peaceman-Rachford, Douglas-Rachford algorithms minimizing the sum two functions when one them is strongly convex. A similar given in more gener...

We consider a sequence of convex integral functionals Fs : W1,p(Ωs) → ℝ and weakly lower semicontinuous and, in general, nonintegral Gs ℝ, where {Ωs} is domains ℝn contained bounded domain Ω ⊂ (n ⩾ 2) p > 1. Along with this, we closed sets Vs = {v ∈ Ms(v) ⩽ 0 a.e. Ωs}, Ms mapping from to the set all functions defined on Ωs. establish conditions under which minimizers minimum values +Gs converge...