Some convergence theorems of non-implicit iteration process with errors for a finite families of I-asymptotically nonexpansive mappings

The purpose of this paper is to study the weak and strong convergence of non-implicit iteration process with errors to a common fixed point for a finite family of I-asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of several authors [1], [2], [7], [8], [9], [10], [11], [12], [13], [14], [17], [19], [22], [23], [24], [25], [26], [27], [28] and [29].     

Weak convergence conditions for Inexact Newton-type methods

We establish a new semilocal convergence results for Inexact Newton-type methods for approximating a locally unique solution of a nonlinear equation in a Banach spaces setting. We show that our sufficient convergence conditions are weaker and the estimates of error bounds are tighter in some cases than in earlier works [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30] and [31]. Special cases and numerical examples are also provided in this study.     

The matching theorems in G-convex spaces with applications

The purpose of this paper is to establish some new matching theorems in G-convex spaces and, as applications, to obtain some new fixed point theorems, section theorems and a minimax theorem in G-convex spaces. The results presented in this paper improve and generalize the corresponding results in [1], [2], [3], [4], [5], [7], [8], [9], [10], [11] and [12].     

Convergence Theory for AOR Method

In this paper we give some sufficient conditions for the convergence of the AOR method, introduced by Hadjidimos [5], which include the ones from [1], [2], [5], [6], [7], [9], [10], [11], [12] and which show that the necessary condition given in [8] for the convergence of the AOR method is not valid. We give general conditions for the class of H-matrices, but they are not always easy to check in practice. Consequently, we give some more practical conditions concerning some subclasses of H-matrices.     

On strong convergence in real Banach spaces obtained by dropping the Lipshitz condition

We consider an implicit iterative process for two finite families of mappings in a real Banach space and prove strong convergence results without using the Lipschitz condition on mappings. Our results mainly improve and extend the recent results of Chang et al. (2001, 2009, 2007) [1], [2], [3], Cho et al. (2005) [4], Gu (2008) [14], Ofoedu (2006) [9], Schu (1991) [13], Zeng (2003, 2005) [20], [21], and Qin et al. (2008) [11], [12].     

Graphs with two isomorphism classes of spanning unicyclic subgraphs

The graphs whose spanning unicyclic subgraphs partition into exactly two isomorphism classes are characterized.This work is a continuation of [6] where graphs with one isomorphism class of spanning unicyclic graphs are characterized. The analogous question for spanning trees was posed in [10] and graphs with one isomorphism class of spanning trees were characterized in [2], [3], [4], [7], [11] while graphs with two isomorphism classes of spanning trees were characterized in [4], [5]. Related topics are treated in [1], [8], [9].     

An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension

We use geometrical combinatorics arguments, including the "hairbrush" argument of Wolff [W1], the x-ray estimates in [W2], [LT], and the sticky/plany/grainy analysis of [KLT], to show that Besicovitch sets in have Minkowski dimension at least for all , where is an absolute constant depending only on n. This complements the results of [KLT], which established the same result for n = 3, and of [B3], [KT], which used arithmetic combinatorics techniques to establish the result for . Unlike the arguments in [KLT], [B3], [KT], our arguments will be purely geometric and do not require arithmetic combinatorics. Submitted: April 2000, Revised version: November 2000.     

Global exponential stability of a class of retarded impulsive differential equations with applications

This paper studies the dynamics of a class of retarded impulsive differential equations (IDE), which generalizes the delayed cellular neural networks (DCNN), delayed bidirectional associative memory (BAM) neural networks and some population growth models. Some sufficient criteria are obtained for the existence and global exponential stability of a unique equilibrium. When the impulsive jumps are absent, our results reduce to its corresponding results for the non-impulsive systems. The approaches are based on Banach’s fixed point theorem, matrix theory and its spectral theory. Due to this method, our results generalize and improve many previous known results such as [3], [5], [6], [9], [17], [18], [23], [32], [38], [43], [51], [52]. Some examples are also included to illustrate the feasibility and effectiveness of the results obtained.     

A new method for solving singular fourth-order boundary value problems with mixed boundary conditions

In [1], [2], [3], [4], [5], [6], [7] and [8], it is very difficult to get reproducing kernel space of problem (1). This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of fourth-order in the new reproducing kernel space. The numerical results are compared with both the exact solution and its n-order derived functions in the example. It is demonstrated that the new method is quite accurate and efficient for fourth-order problems.     

A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions

Summary This paper gives a method for finding sharpa posteriori error bounds for Newton's method under the assumptions of Kantorovich's theorem. On the basis of this method, new error bounds are derived, and comparison is made among the known bounds of Dennis [2], Döring [4], Gragg-Tapia [5], Kantorovich [6, 7], Kornstaedt [9], Lancaster [10], Miel [11–13], Moret [14], Ostrowski [17, 18], Potra [19], and Potra-Pták [20].This paper was written while the author was visiting the Mathematics Research Center, University of Wisconsin-Madison, U.S.A. from March 29, 1985 to October 21, 1985Sponsored by the Ministry of Education in Japan and the United States Army under Contract No. DAAG 29-80-C-0041     

A class of norms of iterative methods for solving systems of linear equations

A new class of norms which generalize norms previously investigated by Young [9, 14], Sheldon [4, 5], Golub [1], Golub and Varga [2], Varga [6], Wachspress [7], Young and Kincaid [12], Young [14], and Kincaid [3] is introduced. Expressions for these norms applied to the matrices associated with various iterative methods are developed.Work on this paper was sponsored by NSF Grant GP-8442 and Army Grant DA-ARO(D)-31-124-G1050 at The University of Texas at Austin.     

Degenerated nonlinear hyperbolic equation with discontinuous coefficients

The partial differential equations with discontinuous coefficients have been extended in various directions by a number of authors [2], [3], [11], [13], [14], [16]. This paper deals with a mixed problem for a degenerated nonlinear hyperbolic equation with discontinuous coefficients.     

RGC n -commutative Δ-semigroups

S is called a δ-semigroup if the lattice of all congruences of S is a chain with respect to inclusion. In the literature there are lots of papers which investigate the δ-semigroups in special classes of semigroups ([1], [3], [5], [6], [10], [11], [12], [14],). In this paper we describe the RGC _n -commutative δ-semigroups.     

Sperner's theorem on maximal-sized antichains and its generalization

This paper generalizes previous work by Sperner [8], Erdös [2], Kleitman [5], Katona [3], DeBruijn et al. [1], and Schönheim [7]. Such generalization not only leads to simple proofs of known results but also sharpens some of these results.     

New results on linearly perturbed polyhedral normal cone mappings

This paper establishes an exact formula for the Fréchet coderivative and some estimates for the Mordukhovich coderivative of the linearly perturbed normal cone mappings in reflexive Banach spaces. In comparison with Nam (2010) [5], Qui (in press) [8], Qui (2011) [7], Trang (2010) [9], the major advantage of our investigation is that here neither the linear independence condition nor the positively linear independence condition are used. Thus, no assumption on the normal vectors of the active constraints at the point in question is needed. Some aspects of the preceding results (Henrion, Mordukhovich and Nam (2010) [3], Nam (2009) [5], Qui (2011) [7], Yao and Yen (2009) [10], Yao and Yen (2009) [11]) are developed.     

平方损失下的可容许估计

设(x)为样本空间,P_θ为其上的分布族,θ∈Θ为参数.欲估计g(θ),损失函数为L(g(θ),d).称R(g(θ),d(X))=EL(g(θ),d(X))为估计d(X)的风险函数.称d_0(X)是g(θ)的可容许估计,如果不存在其它估计d_1(X),使得R(g(θ),d_1(X))≤R(g(θ),d_0(X)),对一切θ∈Θ,且不等号至少对某θ_0∈Θ成立.设在参数空间Θ上建立了σ~-域θ,ξ为(Θ,θ)上σ~-有限测度.称g(θ)的估计δ_0(X)关于ξ是几乎可容     

Gronwall-Bellman type nonlinear delay integral inequalities on time scales

In this paper, some Gronwall-Bellman type nonlinear delay integral inequalities on time scales are established, which provide a handy tool in deriving boundedness of solutions of certain delay dynamic equations on time scales. Our results generalize some of the main results in Lipovan (2006) [1], Pachpatte (2000) [2], Ferreira and Torres (2009) [3], Zhang and Meng (2008) [4], Cheung and Ren (2006) [5], Kim (2009) [6], and some of our results unify continuous and discrete analysis in the literature.     

Gleichverteilte Folgen in lokalkompakten Gruppen

In this paper we consider concepts of uniform distribution in locally compact groups in connection with representation theory. We study questions concerning the existence and quality of uniformly distributed sequences in connection with the structure of general locally compact groups (including also several examples of particular groups), certain separability-conditions, and the structure of the according representation space (the latter primarily for the circle-group). For connections to known concepts the reader is referred to [29], [14], [25], [48], [21], [53]; [19]; [26], [17]; [9]; [3]; [40].

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Herrn Prof. Dr. E. Hlawka zum 60. Geburtstag gewidmet     

Convergence of Directional Methods under mild differentiability and applications

A semilocal convergence analysis for Directional Methods under mild differentiability conditions is provided in this study. Using our idea of recurrent functions, we provide sufficient convergence conditions as well as the corresponding errors bounds. The results are extended to hold in a Hilbert space setting and a favorable comparison is provided with earlier works [6], [7], [8], [9], [10], [11] and [20]. Numerical examples are also provided in this study.     

Linear congruence relations for 2-adic L-series at integers

In the paper we find a further generalization of congruences of the K. Hardy and K. S. Williams [5] type which seems to be a full generalization of congruences of G. Gras [4]. Moreover we extend results of [5], [7], [8], [9] and in part of [6]. We apply ideas and methods of [2], [7] and [9].