arXiv subjects

Nguyen Van Dung

Publications and source records attributed to Nguyen Van Dung.

7 recordsLinked to original sources

arXiv2021

A Stochastic Variance Reduction Algorithm with Bregman Distances for Structured Composite Problems

We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the primal-dual gap is proved under mild conditions on stepsize for the general case. The linear convergence rate is obtained under additional condition like the strong convexity relative to Bregman functions.

math.OC↗

arXiv2021

Convergence analysis of the stochastic reflected forward-backward splitting algorithm

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased estimations of the Lipschitzian operator. We obtain the rate $\mathcal{O}(log(n)/n)$ in expectation for the strongly monotone case, as well as almost sure convergence for the general case. Furthermore, in the context of application to convex-concave saddle point problems, we derive the rate of the primal-dual gap. In particular, we also obtain $\mathcal{O}(1/n)$ rate convergence of the primal-dual gap in the deterministic setting.

math.OC↗

arXiv2019

Further comments on a fixed point theorem in the fractal space

In this paper, we give some further comments to the counterexample and the results of R.~K. Bisht in [R.~K. Bisht. \newblock {Comment on: A new fixed point theorem in the fractal space}. \newblock {\em Indag. Math. (N.S.)}, 29(2):819--823, 2018.].

math.FA↗

arXiv2019

Stability of Euler-Lagrange type cubic functional equations in quasi-Banach spaces

In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form \begin{align*} 2mf(x + my) + 2f(mx - y) = (m^3 + m)[f(x+ y) + f(x - y)] + 2(m^4 - 1)f(y) \end{align*} for all $x,y \in X$, where $m$ is a fixed scalar such that $m \neq 0,1$, and $f$ is a map from a quasi-normed space $X$ to a quasi-Banach space $Y$ over the same field with $X$ by applying the alternative fixed point theorem.

math.FA↗

arXiv2017

On Frink's metrization technique and applications

In this paper, we give a simple counterexample to show again the limits of Frink's~construction and then use Frink's metrization technique to answer two conjectures posed by Berinde and Choban, and to calculate corresponding metrics induced by some $b$-metrics known in the literature. We also use that technique to prove a metrization theorem for 2-generalized metric spaces, and to deduce the Banach contraction principle in $b$-metric spaces and 2-generalized metric spaces from that in metric spaces.

math.GN↗

arXiv2015

Answers to Kirk-Shahzad's questions on strong $b$-metric spaces

In this paper, two open questions on strong $b$-metric spaces posed by Kirk and Shahzad [11, Chapter 12] are investigated. A counter-example is constructed to give a negative answer to the first question, and a theorem on the completion of a strong $b$-metric space is proved to give a positive answer to the second question.

math.GN↗

arXiv2014

A generalization of Ćirić fixed point theorem

In this paper, we state and prove a generalization of Ćirić fixed point theorems in metric space by using a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical fixed point theorems in the literature. Moreover, a multi-valued version for generalized quasi-contraction is also established.

math.GN↗