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Songxiao Li

Publications and source records attributed to Songxiao Li.

At least 37 records · Page 2Linked to original sources
arXiv2020

Several self-adaptive inertial projection algorithms for solving split variational inclusion problems

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed under the effect of self-adaptive stepsizes which does not require information of the norms of the given operators. Some strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, an experimental application is given to illustrate the performances of proposed methods by comparing existing results.

math.OC↗
arXiv2020

Self adaptive inertial extragradient algorithms for solving variational inequality problems

In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for our algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performances of the proposed algorithms and provide a comparison with related ones.

math.OC↗
arXiv2020

An explicit extragradient algorithm for equilibrium problems on Hadamard manifolds

In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the $R$-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm. The results presented in this paper generalize some corresponding known results.

math.OC↗
arXiv2020

An inertial shrinking projection algorithm for split common fixed point problems

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on mappings. Finally, some numerical examples are presented to illustrate the results in this paper.

math.OC↗
arXiv2020

Strong convergence of modified inertial Mann algorithms for nonexpansive mappings

In this paper, we introduce two new modified inertial Mann Halpern and viscosity algorithms for solving fixed point problems. We establish strong convergence theorems under some suitable conditions. Finally, our algorithms are applied to split feasibility problem, convex feasibility problem and location theory. The algorithms and results presented in this paper can summarize and improve corresponding results previously known in this area.

math.OC↗
arXiv2020

Sparse domination of weighted composition operators on weighted Bergman spaces in the upper half-plane

The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the $A_2$ theorem for Calderón-Zygmund operators in harmonic analysis. Using this tool from harmonic analysis, some new characterizations are given for the boundedness and compactness of weighted composition operators acting between weighted Bergman spaces in the upper half plane. Moreover, we establish a new weighted type estimate for the holomorphic Bergman-class functions, for a new class of weights, which is adapted to Sawyer--testing conditions. We also extend our results to the unit ball $\mathbb B$ in $\mathbb C^n$.

math.CV↗
arXiv2019

Weighted Bergman spaces induced by doubling weights in the unit ball of $\mathbb{C}^n$

This paper is devoted to the study of the weighted Bergman space $A_ω^p $ in the unit ball $\mathbb{B}$ of $\mathbb{C}^n$ with doubling weight $ω$ satisfying $$\int_r^1ω(t)dt <C \int_{\frac{1+r}{2}}^1ω(t)dt ,\,\, 0\leq r<1.$$ The $q-$Carleson measures for $A_ω^p$ are characterized in terms of a neat geometric condition involving Carleson block. Some equivalent characterizations for $A_ω^p$ are obtained by using the radial derivative and admissible approach regions. The boundedness and compactness of Volterra integral operator $T_g:A_ω^p\to A_ω^q$ are also investigated in this paper with $0<p\leq q<\infty$, where $$T_gf(z)=\int_0^1 f(tz)\Re g(tz)\frac{dt}{t}, ~~\qquad~~~~f\in H(\mathbb{B}), ~~z\in \mathbb{B}. $$

math.FA↗
arXiv2019

On Invariant Subspaces of Subdecomposable Operators

In this paper, we prove the Mohebi-Radjabalipour Conjecture under a little additional condition, and obtain a new invariant subspace theorem for subdecomposable operators. Our main results contain known results in this topic as special cases. Moreover, the condition in our theorem is really much weaker, much simpler and much more nature than that in the known results.

math.FA↗
arXiv2018

Embedding theorem for Dirichlet type spaces

Using Carleson measure theorem of weighted Bergman spaces, we provide a complete characterization of embedding theorem for Dirichlet type spaces. As an application, we study the Volterra integral operator and multipliers for Dirichlet type spaces.

math.CV↗
arXiv2018

Weighted composition operators on weighted Bergman spaces induced by double weights

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_φ$ on Bergman type spaces $A_ω^p $ with double weight $ω$. Let $X=\{u\in H(D): uC_φ:A_ω^p\to A_ω^p \mbox{ is bounded}\}.$ For some regular weights $ω$, we obtain that $X=H^\infty$ if and only if $φ$ is a finite Blaschke product.

math.CV↗
arXiv2018

Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space

Let $μ$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_μ=(μ_{n+k})_{n,k\geq 0}$ with entries $μ_{n,k}=μ_{n+k}$ induces the operator $$ \mathcal{H}_μ(f)(z)=\sum^\infty_{n=0}\left(\sum^\infty_{k=0}μ_{n,k}a_k\right)z^n $$ on the space of all analytic functions $f(z)=\sum^\infty_{n=0}a_nz^n$ in the unit disk $\mathbb{D}$. In this paper, we characterize the boundedness and compactness of $\mathcal{H}_μ$ from Bloch type spaces to the BMOA and the Bloch space. Moreover we obtain the essential norm of $\mathcal{H}_μ$ from $α$ Bloch type spaces to Bloch space and BMOA.

math.CV↗
arXiv2018

Linear combination of composition operators on $H^\infty$ and the Bloch space

Let $λ_i (i=1,...,k)$ be any nonzero complex scalars and $φ_i (i=1,..,k)$ be any analytic self-maps of the unit disk $\mathbb{D}$. We show that the operator $\sum_{i=1}^kλ_iC_{φ_i}$ is compact on the Bloch space $\mathcal{B}$ if and only if $$\lim_{n\to\infty}\|λ_1φ_1^n+λ_2φ_2^n+...+λ_kφ_k^n\|_{\mathcal{B}}=0.$$ We also study the linear combination of composition operators on the Banach algebra of bounded analytic functions.

math.CV↗