摘要:

The purpose of this paper is to present a systematic treatment of central factorial numbers (cfn), including their main properties, as well as to employ them in a variety of applications. The cfn are related more closely to the Stirling numbers than to the other well-known numbers of Bernoulli, Euler, etc., and they are at least as important as Stirling's numbers, said to be “as important as Bernoulli's, or even more so”.

ISSN:0163-0563    

DOI:10.1080/01630568908816313

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

We give elementary proofs for the existence and uniqueness of the best L1-approximation to a continuous function from the class of convex functions on a closed interval, and describe thebest approximation in terms of certain piecewise linear functions.

ISSN:0163-0563    

DOI:10.1080/01630568908816314

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

Let Cb(s) be the space of real-valued functions F, continuous and bounded or a separable Banach space S, and letbe the subspace of those functions which have bounded and continuous (Fréchet) derivatives up to order r on S. In the special case that S = H is a Hilbert space, Giné and León (1980) have shown that a sequence {Pn} of probability measures on the Bore1 u-algebra of His weakly convergent to some limit measure P on the Whole space Cb(H) iff it is so on the subspace(H) for some r≥1 The aim here i s to establish counterparts for nonsmooth Banach spaces, in particular for the space S = C[0,1] of continuous functions on [0,1]. The approach given hereallows one to equip the qualitative result with rates, expressed in terms of a suitable K-functional, connected with the tightness of {Pn} and Jackson-type inequalities. Applications are given to Donsker's weak invariance principle for independent and dependent random functions as well as to a central limit theorem for martingale difference sequences on Banach spaces.

ISSN:0163-0563    

DOI:10.1080/01630568908816315

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

The problem of determining the temperature or the heat flux on one end of an interval from temperature measurements on the (insulated) other end is ill-posed. For the cases of a semi-infinite or finite time - interval, we obtain stability estimates of logarithmic type under simple a-priori assumptions. If we assume more smoothness, we obtain stability estimates of Hölder type via Tikhonov regularization.

ISSN:0163-0563    

DOI:10.1080/01630568908816316

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

Using a generalization of the chain rule of subdifferential calculus we derive expressions for the conjugate of the difference of functions defined on different spaces. As a consequence we are able to extend PSCHENICHNYI'S formula for (M - N)* such as generalized by HIRIART-URRUTY.

ISSN:0163-0563    

DOI:10.1080/01630568908816317

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

In semi-infinite linear optimization theory, one minimizes <p,v> subject to <B(t),v> ≥for all, where T is usually a compact Hausdorff space. Introducing a new concept of certain pseudocompactness, this paper deals with semi-infinite problems on noncompact spaces T. The Kuhn-Tucker-condition and the Kolmogoroff-criterion are derived and a characterization for strong unicity is given. The problem of best approximation is an application of this theory as is shown in the last part.

ISSN:0163-0563    

DOI:10.1080/01630568908816318

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

An optimal control problem for a parabolic equation when the control parameter is the zero order coefficient of the differential operator is considered. An optimality system is derived. Under a certain sign condition, the problem is solved completely, by proving uniqueness and providing a constructive existence proof for the nonlinear parabolic optimality system.

ISSN:0163-0563    

DOI:10.1080/01630568908816319

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

We consider initial value problems for evolution equations in Banach space E with a small parameter E multiplying the time-derivative term. For such problems we construct difference schemes of a high order of approximation that are uniform with respect to the parameter in (0,1).

ISSN:0163-0563    

DOI:10.1080/01630568908816320

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

A theorem about calculation of topological degree for set-contraotions is presented, and then eigenvectors and nonzero fixed points of strict-set-contractions are inveatigated.

ISSN:0163-0563    

DOI:10.1080/01630568908816321

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630568908816312

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor