• Title, Summary, Keyword: admissible spaces

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FIXED POINTS OF BETTER ADMISSIBLE MAPS ON GENERALIZED CONVEX SPACES

  • Park, Se-Hie
    • Journal of the Korean Mathematical Society
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    • v.37 no.6
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    • pp.885-899
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    • 2000
  • We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

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LEFSCHETZ FIXED POINT THEORY FOR COMPACT ABSORBING CONTRACTIVE ADMISSIBLE MAPS

  • Cho, Yeol-Je;Q'Regan, Donal;Yan, Baoqiang
    • The Pure and Applied Mathematics
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    • v.16 no.1
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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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Existence of Solutions of Integral and Fractional Differential Equations Using α-type Rational F-contractions in Metric-like Spaces

  • Nashine, Hemant Kumar;Kadelburg, Zoran;Agarwal, Ravi P.
    • Kyungpook Mathematical Journal
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    • v.58 no.4
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    • pp.651-675
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    • 2018
  • We present ${\alpha}$-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly ${\alpha}$-admissible mappings. Useful examples illustrate the effectiveness of the presented results. As applications, we obtain sufficient conditions for the existence of solutions of a certain type of integral equations followed by examples of nonlinear fractional differential equations that are verified numerically.

FATOU THEOREM AND EMBEDDING THEOREMS FOR THE MEAN LIPSCHITZ FUNCTIONS ON THE UNIT BALL

  • Cho, Hong-Rae;Lee, Jin-Kee
    • Communications of the Korean Mathematical Society
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    • v.24 no.2
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    • pp.187-195
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    • 2009
  • We investigate the boundary values of the holomorphic mean Lipschitz function. In fact, we prove that the admissible limit exists at every boundary point of the unit ball for the holomorphic mean Lipschitz functions under some assumptions on the Lipschitz order. Moreover, we get embedding theorems of holomorphic mean Lipschitz spaces into Hardy spaces or into the Bloch space on the unit ball in $\mathbb{C}_n$.

A UNIFIED FIXED POINT THEORY OF MULTIMAPS ON TOPOLOGICAL VECTOR SPACES

  • Park, Seh-Ie
    • Journal of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.803-829
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    • 1998
  • We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

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ALGEBRAIC SPECTRAL SUBSPACES OF GENERALIZED SCALAR OPERATORS

  • Han, Hyuk
    • Communications of the Korean Mathematical Society
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    • v.9 no.3
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    • pp.617-627
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    • 1994
  • Algebraic spectral subspaces and admissible operators were introduced by K. B. Laursen and M. M. Neumann in 1988 [L88], [N]. These concepts are useful in automatic continuity problems of intertwining linear operators on Banach spaces. In this paper we characterize the algebraic spectral subspaces of generalized scalar operators. From this characterization we show that generalized scalar operators are admissible. Also we show that doubly power bounded operators are generalized scalar. And using the spectral capacity we show that a generalized scalar operator is decomposable. Then we give an example of an operator which is not admissible but decomposable.

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SADDLE POINTS OF VECTOR-vALUED FUNCTIONS IN TOPOLOGICAL VECTOR SPACES

  • Kim, In-Sook
    • Journal of the Korean Mathematical Society
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    • v.37 no.5
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    • pp.849-856
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    • 2000
  • We give a new saddle point theorem for vector-valued functions on an admissible compact convex set in a topological vector space under weak condition that is the semicontinuity of two function scalarization and acyclicty of the involved sets. As application, we obtain the minimax theorem.

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CHARACTERIZATION OF TEMPERED EXPONENTIAL DICHOTOMIES

  • Barreira, Luis;Rijo, Joao;Valls, Claudia
    • Journal of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.171-194
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    • 2020
  • For a nonautonomous dynamics defined by a sequence of bounded linear operators on a Banach space, we give a characterization of the existence of an exponential dichotomy with respect to a sequence of norms in terms of the invertibility of a certain linear operator between general admissible spaces. This notion of an exponential dichotomy contains as very special cases the notions of uniform, nonuniform and tempered exponential dichotomies. As applications, we detail the consequences of our results for the class of tempered exponential dichotomies, which are ubiquitous in the context of ergodic theory, and we show that the notion of an exponential dichotomy under sufficiently small parameterized perturbations persists and that their stable and unstable spaces are as regular as the perturbation.