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1.
We extend the work of Delong and Imkeller (2010) [6] and [7] concerning backward stochastic differential equations with time delayed generators (delay BSDEs). We give moment and a priori estimates in general Lp-spaces and provide sufficient conditions for the solution of a delay BSDE to exist in Lp. We introduce decoupled systems of SDEs and delay BSDEs (delay FBSDEs) and give sufficient conditions for their variational differentiability. We connect these variational derivatives to the Malliavin derivatives of delay FBSDEs via the usual representation formulas. We conclude with several path regularity results, in particular we extend the classic L2-path regularity to delay FBSDEs.  相似文献   

2.
We provide a new semilocal convergence analysis for generating an inexact Newton method converging to a solution of a nonlinear equation in a Banach space setting. Our analysis is based on our idea of recurrent functions. Our results are compared favorably to earlier ones by others and us (Argyros (2007, 2009) [5] and [6], Argyros and Hilout (2009) [7], Guo (2007) [15], Shen and Li (2008) [18], Li and Shen (2008) [19], Shen and Li (2009) [20]). Numerical examples are provided to show that our results apply, but not earlier ones [15], [18], [19] and [20].  相似文献   

3.
4.
The famous Newton-Kantorovich hypothesis (Kantorovich and Akilov, 1982 [3], Argyros, 2007 [2], Argyros and Hilout, 2009 [7]) has been used for a long time as a sufficient condition for the convergence of Newton’s method to a solution of an equation in connection with the Lipschitz continuity of the Fréchet-derivative of the operator involved. Here, using Lipschitz and center-Lipschitz conditions, and our new idea of recurrent functions, we show that the Newton-Kantorovich hypothesis can be weakened, under the same information. Moreover, the error bounds are tighter than the corresponding ones given by the dominating Newton-Kantorovich theorem (Argyros, 1998 [1]; [2] and [7]; Ezquerro and Hernández, 2002 [11]; [3]; Proinov 2009, 2010 [16] and [17]).Numerical examples including a nonlinear integral equation of Chandrasekhar-type (Chandrasekhar, 1960 [9]), as well as a two boundary value problem with a Green’s kernel (Argyros, 2007 [2]) are also provided in this study.  相似文献   

5.
In this paper, we provide a comprehensive study of coderivative formulas for normal cone mappings. This allows us to derive necessary and sufficient conditions for the Lipschitzian stability of parametric variational inequalities in reflexive Banach spaces. Our development not only gives an answer to the open questions raised in Yao and Yen (2009) [11], but also establishes generalizations and complements of the results given in Henrion et al. (2010) [4] and Yao and Yen (2009) [11] and [12].  相似文献   

6.
We introduce the new idea of recurrent functions to provide a semilocal convergence analysis for an inexact Newton-type method, using outer inverses. It turns out that our sufficient convergence conditions are weaker than in earlier studies in many interesting cases (Argyros, 2004 [5] and [6], Argyros, 2007 [7], Dennis, 1971 [14], Deuflhard and Heindl, 1979 [15], Gutiérrez, 1997 [16], Gutiérrez et al., 1995 [17], Häubler, 1986 [18], Huang, 1993 [19], Kantorovich and Akilov, 1982 [20], Nashed and Chen, 1993 [21], Potra, 1982 [22], Potra, 1985 [23]).  相似文献   

7.
In this paper, we introduce a condition on multivalued mappings which is a multivalued version of condition (Cλ) defined by Garcia-Falset et al. (2011) [3]. It is shown here that some of the classical fixed point theorems for multivalued nonexpansive mappings can be extended to mappings satisfying this condition. Our results generalize the results in Lim (1974), Lami Dozo (1973), Kirk and Massa (1990), Garcia-Falset et al. (2011), Dhompongsa et al. (2009) and Abkar and Eslamian (2010) [4], [5], [6], [3], [7] and [8] and many others.  相似文献   

8.
9.
Let X be a complete CAT(0) space, T be a generalized multivalued nonexpansive mapping, and t be a single valued quasi-nonexpansive mapping. Under the assumption that T and t commute weakly, we shall prove the existence of a common fixed point for them. In this way, we extend and improve a number of recent results obtained by Shahzad (2009) [7] and [12], Shahzad and Markin (2008) [6], and Dhompongsa et al. (2005) [5].  相似文献   

10.
This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N’Guérékata (2009) [6] and [7], Mophou (2010) [8] and [9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations.  相似文献   

11.
We define a logic D capable of expressing dependence of a variable on designated variables only. Thus D has similar goals to the Henkin quantifiers of [4] and the independence friendly logic of [6] that it much resembles. The logic D achieves these goals by realizing the desired dependence declarations of variables on the level of atomic formulas. By [3] and [17], ability to limit dependence relations between variables leads to existential second order expressive power. Our D avoids some difficulties arising in the original independence friendly logic from coupling the dependence declarations with existential quantifiers. As is the case with independence friendly logic, truth of D is definable inside D. We give such a definition for D in the spirit of [11] and [2] and [1].  相似文献   

12.
The fine spectra of lower triangular double-band matrices have been examined by several authors (e.g. [13] and [22]). Here we determine the fine spectra of upper triangular double-band matrices over the sequence spaces c0 and c. Upper triangular double-band matrices are infinite matrices which include the left-shift, averaging and difference operators.  相似文献   

13.
In [4] and [5] the authors introduced the variety SMV of MV-algebras with an internal operator, state MV-algebras. In [2] and [3] the authors gave a stronger version of state MV-algebras, called state-morphism MV-algebras. In this paper we continue the studies presented in [2] and [3] just looking at several proper subvarieties of SMV, obtained by imposing suitable conditions on the behavior of the internal operator.  相似文献   

14.
A finite difference method for a time-dependent convection-diffusion problem in one space dimension is constructed using a Shishkin mesh. In two recent papers (Clavero et al. (2005) [2] and Mukherjee and Natesan (2009) [3]), this method has been shown to be convergent, uniformly in the small diffusion parameter, using somewhat elaborate analytical techniques and under a certain mesh restriction. In the present paper, a much simpler argument is used to prove a higher order of convergence (uniformly in the diffusion parameter) than in [2] and [3] and under a slightly less restrictive condition on the mesh.  相似文献   

15.
In this paper, we prove some decay properties of global solutions for the Navier-Stokes equations in an exterior domain ΩRn, n=2,3.When a domain has a boundary, the pressure term is troublesome since we do not have enough information on the pressure near the boundary. To overcome this difficulty, by multiplying a special form of test functions, we obtain an integral equation. He-Xin (2000) [12] first introduced this method and then Bae-Jin (2006, 2007) [1] and [13] modified their method to obtain better decay rates. Also, Bae-Roh (2009) [11] improved Bae-Jin’s results. Unfortunately, their results were not optimal, because there exists an unpleasant positive small δ in their rates.In this paper, we obtain the following optimal rate without δ,
  相似文献   

16.
In Wang and Xu (2006) [15] and [16] the authors introduced a family of graphs Hn and gave some methods for finding graphs among this family that are determined by their generalized spectra. This paper is a continuation of our previous work. We further show that almost all graphs in Hn are determined by their generalized spectra. This gives some evidences for the conjecture that almost all graphs are determined by their generalized spectra.  相似文献   

17.
We consider infinite Prandtl number convection with rotation which is the basic model in geophysical fluid dynamics. For the rotation free case, the rigorous analysis has been provided by Park (2005, 2007, revised for publication) [5], [6] and [25] under various boundary conditions. By thoroughly investigating we prove in this paper that the solutions bifurcate from the trivial solution u=0 to an attractor ΣR which consists of only one cycle of steady state solutions and is homeomorphic to S1. We also see how intensively the rotation inhibits the onset of convective motion. This bifurcation analysis is based on a new notion of bifurcation, called attractor bifurcation which was developed by Ma and Wang (2005); see [15].  相似文献   

18.
Extending a previous result of Tang [1] we prove the uniqueness of positive radial solutions of Δpu+f(u)=0, subject to Dirichlet boundary conditions on an annulus in Rn with 2<pn, under suitable hypotheses on the nonlinearity f. This argument also provides an alternative proof for the uniqueness of positive solutions of the same problem in a finite ball (see [9]), in the complement of a ball or in the whole space Rn (see [10], [3] and [11]).  相似文献   

19.
This paper studies the conditional quantile regression problem involving the pinball loss. We introduce a concept of τ-quantile of p-average logarithmic type q to complement the previous study by Steinwart and Christman (2008, 2011) [1] and [2]. A new comparison theorem is provided which can be used for further error analysis of some learning algorithms.  相似文献   

20.
The classical existence-and-uniqueness theorem of the solution to a stochastic differential delay equation (SDDE) requires the local Lipschitz condition and the linear growth condition (see e.g. [11], [12] and [20]). The numerical solutions under these conditions have also been discussed intensively (see e.g. [4], [10], [13], [16], [17], [18], [21], [22] and [24]). Recently, Mao and Rassias [14] and [15] established the generalized Khasminskii-type existence-and-uniqueness theorems for SDDEs, where the linear growth condition is no longer imposed. These generalized Khasminskii-type theorems cover a wide class of highly nonlinear SDDEs but these nonlinear SDDEs do not have explicit solutions, whence numerical solutions are required in practice. However, there is so far little numerical theory on SDDEs under these generalized Khasminskii-type conditions. The key aim of this paper is to close this gap.  相似文献   

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