• 제목/요약/키워드: quasi-Banach space

검색결과 42건 처리시간 0.02초

GENERALIZED VECTOR-VALUED VARIATIONAL INEQUALITIES AND FUZZY EXTENSIONS

  • Lee, Byung-Soo;Lee, Gue-Myung;Kim, Do-Sang
    • 대한수학회지
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    • 제33권3호
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    • pp.609-624
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    • 1996
  • Recently, Giannessi [9] firstly introduced the vector-valued variational inequalities in a real Euclidean space. Later Chen et al. [5] intensively discussed vector-valued variational inequalities and vector-valued quasi variationl inequalities in Banach spaces. They [4-8] proved some existence theorems for the solutions of vector-valued variational inequalities and vector-valued quasi-variational inequalities. Lee et al. [14] established the existence theorem for the solutions of vector-valued variational inequalities for multifunctions in reflexive Banach spaces.

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A REMARK ON THE REGULARIZED GAP FUNCTION FOR IQVI

  • Kum, Sangho
    • 충청수학회지
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    • 제28권1호
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    • pp.145-150
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    • 2015
  • Aussel et al. [1] introduced the notion of inverse quasi-variational inequalities (IQVI) by combining quasi-variational inequalities and inverse variational inequalities. Discussions are made in a finite dimensional Euclidean space. In this note, we develop an infinite dimensional version of IQVI by investigating some basic properties of the regularized gap function of IQVI in a Banach space.

GENERALIZED HYERS-ULAM-RASSIAS STABILITY FOR A GENERAL ADDITIVE FUNCTIONAL EQUATION IN QUASI-β-NORMED SPACES

  • Moradlou, Fridoun;Rassias, Themistocles M.
    • 대한수학회보
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    • 제50권6호
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    • pp.2061-2070
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    • 2013
  • In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.

ON ω-CHEBYSHEV SUBSPACES IN BANACH SPACES

  • Shams, Maram;Mazaheri, Hamid;Vaezpour, Sayed Mansour
    • 대한수학회보
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    • 제45권3호
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    • pp.601-606
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    • 2008
  • The purpose of this paper is to introduce and discuss the concept of ${\omega}$-Chebyshev subspaces in Banach spaces. The concept of quasi Chebyshev in Banach space is defined. We show that ${\omega}$-Chebyshevity of subspaces are a new class in approximation theory. In this paper, also we consider orthogonality in normed spaces.

FIXED POINT THEOREMS FOR SET-VALUED MAPS IN QUASI-METRIC SPACES

  • Cho, Seong-Hoon
    • 충청수학회지
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    • 제23권4호
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    • pp.599-608
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    • 2010
  • In this paper, we introduce the concept of generalized weak contractivity for set-valued maps defined on quasi metric spaces. We analyze the existence of fixed points for generalized weakly contractive set-valued maps. And we have Nadler's fixed point theorem and Banach's fixed point theorem in quasi metric spaces. We investigate the convergene of iterate schem of the form $x_{n+1}{\in}Fx_n$ with error estimates.

AN ERROR ANALYSIS FOR A CERTAIN CLASS OF ITERATIVE METHODS

  • Argyros, Ioannis K.
    • Journal of applied mathematics & informatics
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    • 제8권3호
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    • pp.743-753
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    • 2001
  • We provide local convergence results in affine form for inexact Newton-like as well as quasi-Newton iterative methods in a Banach space setting. We use hypotheses on the second or on the first and mth Frechet-derivative (m≥2 an integer) of the operator involved. Our results allow a wider choice of starting points since our radius of convergence can be larger than the corresponding one given in earlier results using hypotheses on the first-Frechet-derivative only. A numerical example is provided to illustrate this fact. Our results apply when the method is, for example, a difference Newton-like or update-Newton method. Furthermore, our results have direct applications to the solution of autonomous differential equations.

PARAMETRIZED GUDERMANNIAN FUNCTION RELIED BANACH SPACE VALUED NEURAL NETWORK MULTIVARIATE APPROXIMATIONS

  • GEORGE A. ANASTASSIOU
    • Journal of Applied and Pure Mathematics
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    • 제5권1_2호
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    • pp.69-93
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    • 2023
  • Here we give multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝN, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a parametrized Gudermannian sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.

STRONG CONVERGENCE FOR THREE CLASSES OF UNIFORMLY EQUI-CONTINUOUS AND ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS

  • Qin, Xiaolong;Su, Yongfu;Shang, Meijuan
    • 대한수학회지
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    • 제45권1호
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    • pp.29-40
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    • 2008
  • In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others.