• Title/Summary/Keyword: quasi-Banach space

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A LOWER ESTIMATE OF THE BANACH-MAZUR DISTANCES ON THE QUASI-NORMED SPACES

  • Kang, JeongHeung
    • Korean Journal of Mathematics
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    • v.7 no.2
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    • pp.207-213
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    • 1999
  • In this paper we estimate a lower bound of the Banach-Mazur distance between a finite dimensional nonlocally convex space and its Banach envelope space by investigating the properties of the nonlocally convex space and the projection constant which are obtained by factoring the identity operator through $l^k_{\infty}$ on the quasi-normed spaces.

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APPROXIMATION OF DRYGAS FUNCTIONAL EQUATION IN QUASI-BANACH SPACE

  • RAVINDER KUMAR SHARMA;SUMIT CHANDOK
    • Journal of applied mathematics & informatics
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    • v.41 no.3
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    • pp.469-485
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    • 2023
  • In this paper, we investigate the Hyers-Ulam-Rassias stability for a Drygas functional equation g(u + v) + g(u - v) = 2g(u) + g(v) + g(-v) in the setting of quasi-Banach space using fixed point approach. Also, we give general results on hyperstability of a Drygas functional equation. The results obtain in this paper extend various previously known results in the setting of quasi-Banach space. Some examples are also illustrated.

ON THE QUADRATIC MAPPING IN GENERALIZED QUASI-BANACH SPACES

  • Park, Choonkil;Jun, Kil-Woung;Lu, Gang
    • Journal of the Chungcheong Mathematical Society
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    • v.19 no.3
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    • pp.263-274
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    • 2006
  • In this paper, we prove the Hyers-Ulam-Rassias stability of the quadratic mapping in generalized quasi-Banach spaces, and of the quadratic mapping in generalized p-Banach spaces.

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GENERALIZED QUASI-BANACH SPACES AND QUASI-(2; p)-NORMED SPACES

  • Park, Choonkil
    • Journal of the Chungcheong Mathematical Society
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    • v.19 no.2
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    • pp.197-206
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    • 2006
  • In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated. We introduce quasi-2-normed spaces and quasi-(2; p)-normed spaces, and investigate the properties of quasi-2-normed spaces and quasi-(2; p)-normed spaces.

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STABILITY OF A MIXED QUADRATIC AND ADDITIVE FUNCTIONAL EQUATION IN QUASI-BANACH SPACES

  • Najati, Abbas;Moradlou, Fridoun
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1177-1194
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    • 2009
  • In this paper we establish the general solution of the functional equation f(2x+y)+f(x-2y)=2f(x+y)+2f(x-y)+f(-x)+f(-y) and investigate the Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

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STABILITY OF A QUADRATIC FUNCTIONAL EQUATION IN QUASI-BANACH SPACES

  • Najati, Abbas;Moradlou, Fridoun
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.587-600
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    • 2008
  • In this paper we establish the general solution and investigate the Hyers-Ulam-Rassias stability of the following functional equation in quasi-Banach spaces. $${\sum\limits_{{{1{\leq}i<j{\leq}4}\limits_{1{\leq}k<l{\leq}4}}\limits_{k,l{\in}I_{ij}}}\;f(x_i+x_j-x_k-x_l)=2\;\sum\limits_{1{\leq}i<j{\leq}4}}\;f(x_i-x_j)$$ where $I_{ij}$={1, 2, 3, 4}\backslash${i, j} for all $1{\leq}i<j{\leq}4$. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.

WEAK AND STRONG CONVERGENCE FOR QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES

  • Kim, Gang-Eun
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.4
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    • pp.799-813
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    • 2012
  • In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

SOLUTION AND STABILITY OF MIXED TYPE FUNCTIONAL EQUATIONS

  • Jun, Kil-Woung;Jung, Il-Sook;Kim, Hark-Mahn
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.4
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    • pp.815-830
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    • 2009
  • In this paper we establish the general solution of the following functional equation with mixed type of quadratic and additive mappings f(mx+y)+f(mx-y)+2f(x)=f(x+y)+f(x-y)+2f(mx), where $m{\geq}2$ is a positive integer, and then investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.

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GENERALIZED QUASI-BANACH SPACES

  • Baak, Choonkil
    • Journal of the Chungcheong Mathematical Society
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    • v.18 no.2
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    • pp.215-222
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    • 2005
  • In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated.

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CONVERGENCE TO COMMON FIXED POINTS FOR A FINITE FAMILY OF GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES

  • Saluja, G.S.
    • East Asian mathematical journal
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    • v.29 no.1
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    • pp.23-37
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    • 2013
  • The purpose of this paper is to study an implicit iteration process with errors and establish weak and strong convergence theorems to converge to common fixed points for a finite family of generalized asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve and generalize some known results from the existing literature.