DSpace Collection: Volume 24 Number 2
http://hdl.handle.net/10525/516
Serdica Mathematical Journal Volume 24, Number 2, 1998The Collection's search engineSearch the Channelsearch
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The Point of Continuity Property: Descriptive Complexity and Ordinal Index
http://hdl.handle.net/10525/558
Title: The Point of Continuity Property: Descriptive Complexity and Ordinal Index<br/><br/>Authors: Bossard, Benoit; López, Ginés<br/><br/>Abstract: Let X be a separable Banach space without the Point ofContinuity Property. When the set of closed subsets of its closed unit ballis equipped with the standard Effros-Borel structure, the set of those whichhave the Point of Continuity Property is non-Borel. We also prove that,for any separable Banach space X, the oscillation rank of the identity onX (an ordinal index which quantifies the Point of Continuity Property) isdetermined by the subspaces of X with a finite-dimensional decomposition.If X does not contain l1 , subspaces with basis suffice. If X ∗ is separable,one can even restrict to subspaces with shrinking basis.<br/><br/>Description: ∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142Fragmentability of the Dual of a Banach Space with Smooth Bump
http://hdl.handle.net/10525/557
Title: Fragmentability of the Dual of a Banach Space with Smooth Bump<br/><br/>Authors: Kortezov, I.<br/><br/>Abstract: We prove that if a Banach space X admits a Lipschitz β-smoothbump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating atopology, which is stronger than the τβ -topology. We also use this to provethat if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X issigma-fragmentable.New Symmetric (61,16,4) Designs Invariant Under the Dihedral Group of Order 10
http://hdl.handle.net/10525/556
Title: New Symmetric (61,16,4) Designs Invariant Under the Dihedral Group of Order 10<br/><br/>Authors: Landjev, Ivan; Topalova, Svetlana<br/><br/>Abstract: In this note we construct five new symmetric 2-(61,16,4) designs invariant under the dihedral group of order 10. As a by-product weobtain 25 new residual 2-(45,12,4) designs. The automorphism groups of allnew designs are computed.<br/><br/>Description: ∗ This work has been partially supported by the Bulgarian NSF under Contract No. I-506/1995.Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces
http://hdl.handle.net/10525/555
Title: Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces<br/><br/>Authors: Chowdhury, Mohammad<br/><br/>Abstract: Existence theorems of generalized variational inequalities andgeneralized complementarity problems are obtained in topological vectorspaces for demi operators which are upper hemicontinuous along line segments in a convex set X. Fixed point theorems are also given in Hilbertspaces for set-valued operators T which are upper hemicontinuous alongline segments in X such that I − T are demi operators.<br/><br/>Description: ∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses
http://hdl.handle.net/10525/554
Title: Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses<br/><br/>Authors: Plotnikov, V.; Kitanov, P.<br/><br/>Abstract: In this article on quasidifferential equation with non-fixed timeof impulses we consider the continuous dependence of the solutions on theinitial conditions as well as the mappings defined by these equations. Weprove general theorems for quasidifferential equations from which followscorresponding results for differential equations, differential inclusion andequations with Hukuhara derivative.Three Spaces Problem for Lyapunov Theorem on Vector Measure
http://hdl.handle.net/10525/553
Title: Three Spaces Problem for Lyapunov Theorem on Vector Measure<br/><br/>Authors: Kadets, V.; Vladimirskaya, O.<br/><br/>Abstract: It is proved that a Banach space X has the Lyapunov property if its subspace Y and the quotient space X/Y have it.Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations
http://hdl.handle.net/10525/552
Title: Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations<br/><br/>Authors: Stamov, Gani<br/><br/>Abstract: Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.