• 제목/요약/키워드: Frechet space

검색결과 23건 처리시간 0.023초

A PROOF OF A CONVEX-VALUED SELECTION THEOREM WITH THE CODOMAIN OF A FRECHET SPACE

  • Cho, Myung-Hyun;Kim, Jun-Hui
    • 대한수학회논문집
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    • 제16권2호
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    • pp.277-285
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    • 2001
  • The purpose of this paper is to give a proof of a generalized convex-valued selection theorem which is given by weakening a Banach space to a completely metrizable locally convex topological vector space, i.e., a Frechet space. We also develop the properties of upper semi-continuous singlevalued mapping to those of upper semi-continuous multivalued mappings. These properties wil be applied in our further consideraations of selection theorems.

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RANDOM FIXED POINT THEOREMS FOR *-NONEXPANSIVE OPERATORS IN FRECHET SPACES

  • Abdul, Rahim-Khan;Nawab, Hussain
    • 대한수학회지
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    • 제39권1호
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    • pp.51-60
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    • 2002
  • Some random fixed point theorems for nonexpansive and *-nonexpansive random operators defined on convex and star-shaped sets in a Frechet space are proved. Our work extends recent results of Beg and Shahzad and Tan and Yaun to noncontinuous multivalued random operators, sets analogue to an earlier result of Itoh and provides a random version of a deterministic fixed point theorem due to Singh and Chen.

PROJECTIVE LIMIT OF A SEQUENCE OF BANACH FUNCTION ALGEBRAS AS A FRECHET FUNCTION ALGEBRA

  • Sady. F.
    • 대한수학회보
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    • 제39권2호
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    • pp.259-267
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    • 2002
  • Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

CONCERNING THE RADIUS OF CONVERGENCE OF NEWTON'S METHOD AND APPLICATIONS

  • Argyros, Ioannis K.
    • Journal of applied mathematics & informatics
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    • 제6권3호
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    • pp.685-696
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    • 1999
  • We present local and semilocal convergence results for New-ton's method in a Banach space setting. In particular using Lipschitz-type assumptions on the second Frechet-derivative we find results con-cerning the radius of convergence of Newton's method. Such results are useful in the context of predictor-corrector continuation procedures. Finally we provide numerical examples to show that our results can ap-ply where earlier ones using Lipschitz assumption on the first Frechet-derivative fail.

SEMILOCAL CONVERGENCE THEOREMS FOR A CERTAIN CLASS OF ITERATIVE PROCEDURES

  • Ioannis K. Argyros
    • Journal of applied mathematics & informatics
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    • 제7권1호
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    • pp.29-40
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    • 2000
  • We provide semilocal convergence theorems for Newton-like methods in Banach space using outer and generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Frechet-derivative. This way our Newton-Kantorovich hypotheses differ from earlier ones. Our results can be used to solve undetermined systems, nonlinear least square problems and ill-posed nonlinear operator equations.

AFFINE INVARIANT LOCAL CONVERGENCE THEOREMS FOR INEXACT NEWTON-LIKE METHODS

  • Argyros, Ioannis K.
    • Journal of applied mathematics & informatics
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    • 제6권2호
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    • pp.393-406
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    • 1999
  • Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the second. Radius of con-vergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivation our radius of convergence results are derived. Results involving superlinear convergence and known to be true or inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivative our radius of conver-gence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also pro-vided to show that our radius of convergence is larger then the one in [10].

A LOCAL APPROXIMATION METHOD FOR THE SOLUTION OF K-POSITIVE DEFINITE OPERATOR EQUATIONS

  • Chidume, C.E.;Aneke, S.J.
    • 대한수학회보
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    • 제40권4호
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    • pp.603-611
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    • 2003
  • In this paper we extend the definition of K-positive definite operators from linear to Frechet differentiable operators. Under this setting, we derive from the inverse function theorem a local existence and approximation results corresponding to those of Theorems land 2 of the authors [8], in an arbitrary real Banach space. Furthermore, an asymptotically K-positive definite operator is introduced and a simplified iteration sequence which converges to the unique solution of an asymptotically K-positive definite operator equation is constructed.

LEFSCHETZ FIXED POINT THEORY FOR COMPACT ABSORBING CONTRACTIVE ADMISSIBLE MAPS

  • Cho, Yeol-Je;Q'Regan, Donal;Yan, Baoqiang
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제16권1호
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    • pp.69-83
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    • 2009
  • New Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Frechet spaces are presented. Also we present new results for condensing maps with a compact attractor. The proof relies on fixed point theory in Banach spaces and viewing a Frechet space as the projective limit of a sequence of Banach spaces.

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LOCAL CONVERGENCE THEOREMS FOR NEWTON METHODS

  • Argyros, Ioannis K.
    • Journal of applied mathematics & informatics
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    • 제8권2호
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    • pp.345-360
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    • 2001
  • Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the mth(m≥2 an integer). Radius of convergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover, we show that under hypotheses on the mth Frechet-derivative our radius of convergence can sometimes be larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also provided to show that our radius of convergence is larger than the one in [10].

CHEYSHEFF-HALLEY-LIKE METHODS IN BANACH SPACES

  • Argyros, Ioannis-K.
    • Journal of applied mathematics & informatics
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    • 제4권1호
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    • pp.83-108
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    • 1997
  • Chebysheff-Halley methods are probably the best known cubically convergent iterative procedures for solving nonlinear equa-tions. These methods however require an evaluation of the second Frechet-derivative at each step which means a number of function eval-uations proportional to the cube of the dimension of the space. To re-duce the computational cost we replace the second Frechet derivative with a fixed bounded bilinear operator. Using the majorant method and Newton-Kantorovich type hypotheses we provide sufficient condi-tions for the convergence of our method to a locally unique solution of a nonlinear equation in Banach space. Our method is shown to be faster than Newton's method under the same computational cost. Finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant-flux emerging from a plane radiation field.