• 제목/요약/키워드: Space approximation

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A NOTE ON APPROXIMATION PROPERTIES OF BANACH SPACES

  • Cho, Chong-Man
    • Communications of the Korean Mathematical Society
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    • v.9 no.2
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    • pp.293-298
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    • 1994
  • It is well known that the approximation property and the compact approximation property are not hereditary properties; that is, a closed subspace M of a Banach space X with the (compact) approximation property need not have the (compact) approximation property. In 1973, A. Davie [2] proved that for each 2 < p < $\infty$, there is a closed subspace $Y_{p}$ of $\ell_{p}$ which does not have the approximation property. In fact, the space Davie constructed even fails to have a weaker property, the compact approximation property. In 1991, A. Lima [12] proved that if X is a Banach space with the approximation property and a closed subspace M of X is locally $\lambda$-complemented in X for some $1\leq\lambda < $\infty$, then M has the approximation property.(omitted)

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COMMON FIXED POINT THEOREM AND INVARIANT APPROXIMATION IN COMPLETE LINEAR METRIC SPACES

  • Nashine, Hemant Kumar
    • East Asian mathematical journal
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    • v.28 no.5
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    • pp.533-541
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    • 2012
  • A common fixed point result of Gregus type for subcompatible mappings defined on a complete linear metric space is obtained. The considered underlying space is generalized from Banach space to complete linear metric spaces, which include Banach space and complete metrizable locally convex spaces. Invariant approximation results have also been determined as its application.

A NOTE ON GREEDY ALGORITHM

  • Hahm, Nahm-Woo;Hong, Bum-Il
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.2
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    • pp.293-302
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    • 2001
  • We improve the greedy algorithm which is one of the general convergence criterion for certain iterative sequence in a given space by building a constructive greedy algorithm on a normed linear space using an arithmetic average of elements. We also show the degree of approximation order is still $Ο(1\sqrt{\n}$) by a bounded linear functional defined on a bounded subset of a normed linear space which offers a good approximation method for neural networks.

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Best Approximation Result in Locally Convex Space

  • Nashine, Hemant Kumar
    • Kyungpook Mathematical Journal
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    • v.46 no.3
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    • pp.389-397
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    • 2006
  • A fixed point theorem of Singh and Singh [10] is generalized to locally convex spaces and the new result is applied to extend a result on invariant approximation of Jungck and Sessa [5].

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ON RELATIONSHIPS AMONG INTUITIONISTIC FUZZY APPROXIMATION OPERATORS, INTUITIONISTIC FUZZY TOPOLOGY AND INTUITIONISTIC FUZZY AUTOMATA

  • Tiwari, S.P.
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.99-107
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    • 2010
  • This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X, R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approximation space X (i.e., a set X with a reflexive and transitive relation on it), which turns out to be an intuitionistic fuzzy closure operator. This intuitionistic fuzzy closure operator gives rise to two saturated fuzzy topologies on X and it turns out that all the level topologies of one of the fuzzy topology coincide and equal to the topology analogously induced on X by a crisp approximation operator. These observations are then applied to intuitionistic fuzzy automata.

IMPLICIT DIFFERENCE APPROXIMATION FOR THE TWO-DIMENSIONAL SPACE-TIME FRACTIONAL DIFFUSION EQUATION

  • Zhuang, Pinghui;Liu, Fawang
    • Journal of applied mathematics & informatics
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    • v.25 no.1_2
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    • pp.269-282
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    • 2007
  • In this paper, we consider a two-dimensional fractional space-time diffusion equation (2DFSTDE) on a finite domain. We examine an implicit difference approximation to solve the 2DFSTDE. Stability and convergence of the method are discussed. Some numerical examples are presented to show the application of the present technique.

APPROXIMATION THEOREM FOR CONTRACTION C-SEMIGROUPS

  • Lee, Young S.
    • Korean Journal of Mathematics
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    • v.18 no.3
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    • pp.253-259
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    • 2010
  • In this paper we establish approximation of contraction C-semigroups on the extrapolation space $X^C$, by showing the equicontinuity of contraction C-semigroups on $X^C$.

THE SEPARABLE WEAK BOUNDED APPROXIMATION PROPERTY

  • Lee, Keun Young
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.1
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    • pp.69-83
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    • 2015
  • In this paper we introduce and study the separable weak bounded approximation properties which is strictly stronger than the approximation property and but weaker than the bounded approximation property. It provides new sufficient conditions for the metric approximation property for a dual Banach space.