关于广义Φ-压缩映射几种迭代序列收敛的等价性

在广义Φ-压缩映射条件下,分别得到了Picard迭代序列与Krasnoselskii迭代序列以及Mann迭代序列与Ishikawa迭代序列收敛的等价性.     

快速ESPRIT谐波集检测算法

在各种高分辨谐波检测算法中,TLS-ESPRIT估计精度较高,因不需要谱峰搜索而具有较小的运算量。提出了一种快速ESPRIT算法,在不降低谱估计性能条件下,进一步减小了运算量。快速ESPRIT算法所需采样时间短,仅需两次特征值分解。分析表明,此算法可以检测不同飞行状态的直升机声信号谐波集,是一种实时性好、有效实用的目标谱集探测方法。     

Submanifolds that are level sets of solutions to a second-order elliptic PDE

We consider the problem of characterizing which noncompact hypersurfaces in Rⁿ${\mathbb{R}}^n$ can be regular level sets of a harmonic function modulo a C^∞$C^{\infty }$ diffeomorphism, as well as certain generalizations to other PDEs. We prove a versatile sufficient condition that shows, in particular, that any nonsingular algebraic hypersurface whose connected components are all noncompact can be transformed onto a union of components of the zero set of a harmonic function via a diffeomorphism of Rⁿ${\mathbb{R}}^n$. The technique we use combines robust but not explicit local constructions with appropriate global approximation theorems. In view of applications to a problem posed by Berry and Dennis, intersections of level sets are also studied.     

Lie Triple Derivable Mappings on Rings

Let ? be a ring containing a nontrivial idempotent. In this article, under a mild condition on ?, we prove that if δ is a Lie triple derivable mapping from ? into ?, then there exists a Z _{A, B} (depending on A and B) in its centre 𝒵(?) such that δ(A + B) = δ(A) + δ(B) + Z _{A, B} . In particular, let ? be a prime ring of characteristic not 2 containing a nontrivial idempotent. It is shown that, under some mild conditions on ?, if δ is a Lie triple derivable mapping from ? into ?, then δ = D + τ, where D is an additive derivation from ? into its central closure T and τ is a mapping from ? into its extended centroid 𝒞 such that τ(A + B) = τ(A) + τ(B) + Z _{A, B} and τ([[A, B], C]) = 0 for all A, B, C ∈ ?.     

Projection iterative methods for solving some systems of general nonconvex variational inequalities

In this article, we introduce and consider a new system of general nonconvex variational inequalities involving four different operators. We use the projection operator technique to establish the equivalence between the system of general nonconvex variational inequalities and the fixed points problem. This alternative equivalent formulation is used to suggest and analyse some new explicit iterative methods for this system of nonconvex variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of nonconvex variational inequalities, variational inequalities and related optimization problems as special cases, results obtained in this article continue to hold for these problems. Our results can be viewed as a refinement and an improvement of the previously known results for variational inequalities.     

Inverse problems for differential operators on trees with general matching conditions

Sturm–Liouville differential operators on compact trees with general matching conditions in internal vertices are studied. We establish properties of the spectral characteristics and investigate three inverse problems of recovering the operator either from the so-called Weyl functions, or from discrete spectral data or from a system of spectra. For these inverse problems, we prove the corresponding uniqueness theorems and obtain procedures for constructing their solutions by the method of spectral mappings.     

Hybrid Proximal-Type and Hybrid Shrinking Projection Algorithms for Equilibrium Problems,Maximal Monotone Operators,and Relatively Nonexpansive Mappings

In this article, we introduce two hybrid proximal-type algorithms and two hybrid shrinking projection algorithms by using the hybrid proximal-type method and the hybrid shrinking projection method, respectively, for finding a common element of the set of solutions of an equilibrium problem, the set of fixed points of a relatively nonexpansive mapping, and the set of solutions to the equation 0 ∈ Tx for a maximal monotone operator T defined on a uniformly smooth and uniformly convex Banach space. The strong convergence of the sequences generated by the proposed algorithms is established. Our results improve and generalize several known results in the literature.     

Algorithms for Solutions of Variational Inequalities in the Set of Common Fixed Points of Finite Family of λ-Strictly Pseudocontractive Mappings

In this article, we introduce an algorithm which has strong convergence for solving the variational inequality problem for η-inverse strongly accretive mappings in the set of common fixed points of finite family of λ-strictly pseudocontractive mappings in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.     

A QUANTITATIVE VERSION OF A THEOREM DUE TO BORWEIN-REICH-SHAFRIR

We give a quantitative analysis of a result due to Borwein, Reich and Shafrir on the asymptotic behaviour of the general Krasnoselski-Mann iteration for nonexpansive self-mappings of convex sets in arbitrary normed spaces. Besides providing explicit bounds we also get new qualitative results concerning the independence of the rate of asymptotic regularity of that iteration from various input data. In the special case of bounded convex sets, where by well-known results of Ishikawa, Edelstein/O'Brien and Goebel/Kirk the norm of the iteration converges to zero, we obtain uniform bounds which do not depend on the starting point of the iteration and the nonexpansive function, but only depend on the error ε, an upper bound on the diameter of C and some very general information on the sequence of scalars λ _k used in the iteration. Only in the special situation, where λ _k := λ is constant, uniform bounds were known in that bounded case. For the unbounded case, no quantitative information was known before. Our results were obtained in a case study of analysing non-effective proofs in analysis by certain logical methods. General logical meta-theorems of the author guarantee (at least under some additional restrictions) the extractability of such bounds from proofs of a certain kind and provide an algorithm to extract them. Our results in the present paper (which we present here without any reference to that logical background) were found by applying that method to the original proof of the Borwein/Reich/Shafrir theorem. The general logical method which led to these results will be discussed (with further examples) in [22] Kohlenbach, U. On the computational content of the Krasnoselski and Ishikawa fixed point theorems. Proceedings of the Fourth Workshop on Computability and Complexity in Analysis. San Sebastian. Edited by: Blanck, J., Brattka, V. and Hertling, P. Springer LNCS 2064.  [Google Scholar].