DSpace Collection: Volume 26 Number 4
http://hdl.handle.net/10525/401
Serdica Mathematical Journal Volume 26, Number 4, 2000The Collection's search engineSearch the Channelsearch
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Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis
http://hdl.handle.net/10525/425
Title: Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis<br/><br/>Authors: Rychter, Jan<br/><br/>Abstract: It is shown that a Banach space X admits an equivalent uniformlyGateaux differentiable norm if it has an unconditional basis and X*admits an equivalent norm which is uniformly rotund in every direction.<br/><br/>Description: *Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a partof the author’s MSc thesis written under the supervison of Professor V. Zizler.The Space of Differences of Convex Functions on [0, 1]
http://hdl.handle.net/10525/424
Title: The Space of Differences of Convex Functions on [0, 1]<br/><br/>Authors: Zippin, M.<br/><br/>Abstract: The space K[0, 1] of differences of convex functions on theclosed interval [0, 1] is investigated as a dual Banach space. It is provedthat a continuous function f on [0, 1] belongs to K[0, 1]<br/><br/>Description: ∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University,College Station, Texas, 2000. Research partially supported by the Edmund Landau Centerfor Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation(Germany).Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations
http://hdl.handle.net/10525/423
Title: Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations<br/><br/>Authors: Karandjulov, L.; Stoyanova, Y.<br/><br/>Abstract: A boundary-value problems for almost nonlinear singularlyperturbed systems of ordinary differential equations are considered. An asymptoticsolution is constructed under some assumption and using boundaryfunctions and generalized inverse matrix and projectors.Asplund Functions and Projectional Resolutions of the Identity
http://hdl.handle.net/10525/422
Title: Asplund Functions and Projectional Resolutions of the Identity<br/><br/>Authors: Zemek, Martin<br/><br/>Abstract: We further develop the theory of the so called Asplund functions,recently introduced and studied by W. K. Tang. Let f be an Asplundfunction on a Banach space X. We prove that (i) the subspaceY := sp ∂f(X) has a projectional resolution of the identity, and that (ii) ifX is weakly Lindel¨of determined, then X admits a projectional resolution ofthe identity such that the adjoint projections restricted to Y form a projectionalresolution of the identity on Y , and the dual X* admits an equivalentdual norm such that its restriction to Y is locally uniformly rotund.<br/><br/>Description: *Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by theGrant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets
http://hdl.handle.net/10525/421
Title: A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets<br/><br/>Authors: Ivanov, M.; Zlateva, N.<br/><br/>Abstract: We consider the question whether the assumption of convexityof the set involved in Clarke-Ledyaev inequality can be relaxed. In the casewhen the point is outside the convex hull of the set we show that Clarke-Ledyaevtype inequality holds if and only if there is certain geometrical relation between the point and the set.