• Title/Summary/Keyword: M spaces

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Fixed point iterations for quasi-contractive maps in uniformly smooth banach spaces

  • Chidume, C.E.;Osilike, M.O.
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.2
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    • pp.201-212
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    • 1993
  • It is our purpose in this paper to first establish an inequality in real uniformly smooth Banach spaces with modulus of smoothness of power type q > 1 that generalizes a well known Hilbert space inequality. Using our inequality, we shall then extend the above result of Qihou [15] on the Ishikawa iteration process from Hilbert spaces to these much more general Banach spaces. Furthermore, we shall prove that the Mann iteration process converges strongly to the unique fixed point of a quasi-contractive map in this general setting. No compactness assumption on K is required in our theorems.

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AN EXTERESION THEOREM FOR THE FOLLAND-STEIN SPACES

  • Kim, Yonne-Mi
    • Communications of the Korean Mathematical Society
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    • v.10 no.1
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    • pp.49-55
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    • 1995
  • This paper is the third of a series in which smoothness properties of function in several variables are discussed. The germ of the whole theory was laid in the works by Folland and Stein [4]. On nilpotent Lie groups, they difined analogues of the classical $L^p$ Sobolev or potential spaces in terms of fractional powers of sub-Laplacian, L and extended several basic theorems from the Euclidean theory of differentaiability to these spaces: interpolation properties, boundedness of singular integrals,..., and imbeding theorems. In this paper we study the analogue to the extension theorem for the Folland-Stein spaces. The analogue to Stein's restriction theorem were studied by M. Mekias [5] and Y.M. Kim [6]. First, we have the space of Bessel potentials on the Heisenberg group introduced by Folland [4].

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NONLINEAR CONTRACTIONS IN PARTIALLY ORDERED QUASI b-METRIC SPACES

  • Shah, Masood Hussain;Hussain, Nawab
    • Communications of the Korean Mathematical Society
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    • v.27 no.1
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    • pp.117-128
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    • 2012
  • Using the concept of a g-monotone mapping we prove some common fixed point theorems for g-non-decreasing mappings which satisfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces. The new theorems are generalizations of very recent fixed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, [Monotone generalized nonlinear contractions in partailly ordered metric spaces, Fixed Point Theory Appl. (2008), article, ID-131294] and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan [Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8].

SPECTRAL PROPERTIES OF VOLTERRA-TYPE INTEGRAL OPERATORS ON FOCK-SOBOLEV SPACES

  • Mengestie, Tesfa
    • Journal of the Korean Mathematical Society
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    • v.54 no.6
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    • pp.1801-1816
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    • 2017
  • We study some spectral properties of Volterra-type integral operators $V_g$ and $I_g$ with holomorphic symbol g on the Fock-Sobolev spaces ${\mathcal{F}}^p_{{\psi}m}$. We showed that $V_g$ is bounded on ${\mathcal{F}}^p_{{\psi}m}$ if and only if g is a complex polynomial of degree not exceeding two, while compactness of $V_g$ is described by degree of g being not bigger than one. We also identified all those positive numbers p for which the operator $V_g$ belongs to the Schatten $S_p$ classes. Finally, we characterize the spectrum of $V_g$ in terms of a closed disk of radius twice the coefficient of the highest degree term in a polynomial expansion of g.

FUNCTIONS ATTAINING THE SUPREMUM AND ISOMORPHIC PROPERTIES OF A BANACH SPACE

  • D. Acosta, Maria ;Becerra Guerrero, Julio ;Ruiz Galan, Manuel
    • Journal of the Korean Mathematical Society
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    • v.41 no.1
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    • pp.21-38
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    • 2004
  • We prove that a Banach space that is convex-transitive and such that for some element u in the unit sphere, and for every subspace Μ containing u, it happens that the subset of norm attaining functionals on Μ is second Baire category in $M^{*}$ is, in fact, almost-transitive and superreflexive. We also obtain a characterization of finite-dimensional spaces in terms of functions that attain their supremum: a Banach space is finite-dimensional if, for every equivalent norm, every rank-one operator attains its numerical radius. Finally, we describe the subset of norm attaining functionals on a space isomorphic to $\ell$$_1$, where the norm is the restriction of a Luxembourg norm on $L_1$. In fact, the subset of norm attaining functionals for this norm coincides with the subset of norm attaining functionals for the usual norm.m.

ESSENTIAL NORMS OF INTEGRAL OPERATORS

  • Mengestie, Tesfa
    • Journal of the Korean Mathematical Society
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    • v.56 no.2
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    • pp.523-537
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    • 2019
  • We estimate the essential norms of Volterra-type integral operators $V_g$ and $I_g$, and multiplication operators $M_g$ with holomorphic symbols g on a large class of generalized Fock spaces on the complex plane ${\mathbb{C}}$. The weights defining these spaces are radial and subjected to a mild smoothness conditions. In addition, we assume that the weights decay faster than the classical Gaussian weight. Our main result estimates the essential norms of $V_g$ in terms of an asymptotic upper bound of a quantity involving the inducing symbol g and the weight function, while the essential norms of $M_g$ and $I_g$ are shown to be comparable to their operator norms. As a means to prove our main results, we first characterized the compact composition operators acting on the spaces which is interest of its own.

WEAKLY BERWALD SPACE WITH A SPECIAL (α, β)-METRIC

  • PRADEEP KUMAR;AJAYKUMAR AR
    • Honam Mathematical Journal
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    • v.45 no.3
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    • pp.491-502
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    • 2023
  • As a generalization of Berwald spaces, we have the ideas of Douglas spaces and Landsberg spaces. S. Bacso defined a weakly-Berwald space as another generalization of Berwald spaces. In 1972, Matsumoto proposed the (α, β) metric, which is a Finsler metric derived from a Riemannian metric α and a differential 1-form β. In this paper, we investigated an important class of (α, β)-metrics of the form $F={\mu}_1\alpha+{\mu}_2\beta+{\mu}_3\frac{\beta^2}{\alpha}$, which is recognized as a special form of the first approximate Matsumoto metric on an n-dimensional manifold, and we obtain the criteria for such metrics to be weakly-Berwald metrics. A Finsler space with a special (α, β)-metric is a weakly Berwald space if and only if Bmm is a 1-form. We have shown that under certain geometric and algebraic circumstances, it transforms into a weakly Berwald space.

An Analysis of Urban Open Space with Geographic Information Systems - A Case Study of Ansan City, Korea - (지리정보체계를 이용한 안산시의 오픈스페이스 분석)

  • 서동조;박종화
    • Korean Journal of Remote Sensing
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    • v.6 no.2
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    • pp.89-113
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    • 1990
  • The purpose of this study is to develop means to apply GIS and remote sensing technology to the analysis of Korean urban open spaces. To achieve this objective, a framework of analysis of urban open spaces was developed, and then the framework was applied for the evaluation of the potential and suitability of open spaces of Ansan City, which is a new town developed to accomodate industries relocation from Seoul, Korea, mainly due to their pollution problems. The software used in this study are IDRISI, a grid-based GIS, and KMIPS, a remote sensing analysis system. Both packages are based on IBM PC/AT computers with Microsoft DOS. Landsat MSS and TM data were used for the land use classification, land use change detection, and analysis of transformed vegetation indices. The size of the geographic data base is 110 rows and 150 columns with the spatial resolution of 100m$\times$100m. The framework of analysis includes both quanititative and qualitative analysis of open spaces. The quantitative analysis includes size and distribution of open spaces, urban develpment of open spaces, and the degree of vegree of vegetation removal of the study area. The qualitative analysis includes evaluative criteria for primary productivity of land, park use potential, major visual resources, and urban environmental control. The findings of this study can be summarized as follows. First, the size of builtup areas increased 18.73km$^2$, while the size of forest land decreased 10.86km$^2$ during last ten years. Agricultural lands maintained its size, but shifted toward outside of the city into forest. Second, the potential of open spaces for park use is limited mainly due to their lack of accessibility and connectivity among open spaces, in spite of ample acreage and good site conditions. Third, major landscape elements and historic sites should be connected to the open space system of the city by new accesses and buffers.

ITERATIVE SOLUTION OF NONLINEAR EQUATIONS WITH STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES

  • Jeong, Jae-Ug
    • Journal of applied mathematics & informatics
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    • v.7 no.2
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    • pp.605-615
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    • 2000
  • Let E be a real Banach space with property (U,${\lambda}$,m+1,m);${\lambda}{\ge}$0; m${\in}N$, and let C be a nonempty closed convex and bounded subset of E. Suppose T: $C{\leftrightarro}C$ is a strongly accretive map, It is proved that each of the two well known fixed point iteration methods( the Mann and Ishikawa iteration methods.), under suitable conditions , converges strongly to a solution of the equation Tx=f.