• Title/Summary/Keyword: Convergent sequence

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ON PARANORMED TYPE p-ABSOLUTELY SUMMABLE UNCERTAIN SEQUENCE SPACES DEFINED BY ORLICZ FUNCTIONS

  • Nath, Pankaj Kumar;Tripathy, Binod Chandra
    • Communications of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.121-134
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    • 2021
  • In this paper we introduce the notion of paranormed p-absolutely convergent and paranormed Cesro summable sequences of complex uncertain variables with respect to measure, mean, distribution etc. defined by on Orlicz function. We have established some relationships among these notions as well as with other classes of complex uncertain variables.

AN IMPROVED EXPONENTIAL REGULA FALSI METHODS WITH CUBIC CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

  • Ibrahim, S.A. Hoda
    • Journal of applied mathematics & informatics
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    • v.28 no.5_6
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    • pp.1467-1476
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    • 2010
  • The aim of this paper is to propose a cubic convergent regula falsi iterative method for solving the nonlinear equation f(x) = 0, where f : [a,b] $\subset$ R $\rightarrow$ R is a continuously differentiable. In [3,6] a quadratically convergent regula falsi iterative methods for solving this nonlinear equations is proposed. It is shown there that both the sequences of diameters and iterative points sequence converge to zero simultaneously. So The aim of this paper is to accelerate further the convergence of these methods from quadratic to cubic. This is done by replacing the parameter p in the iteration of [3,5,6] by a function p(x) defined suitably. The convergence analysis is carried out for the method. The method is tested on number of numerical examples and results obtained shows that our methods are better and more effective and comparable to well-known methods.

A Note on Statistically Monotonic and Bounded Sequences of Fuzzy Numbers

  • Hong, Dug-Hun;Kim, Kyung-Tae
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.2
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    • pp.657-659
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    • 2006
  • This note gives a counterexample showing that a main theorem of Aytal and Pehliven's (Information Sciences 176 (2006) 734-744) result on statically monotonic and bounded sequences of fuzzy numbers is not valid.

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ON THE SPECTRAL RADIUS AND INVERTIBILITY OF CERTAIN ELEMENTS IN BANACH ALGEBRA

  • Park, Kyon-Hong;Kim, Byung-Do
    • Journal of applied mathematics & informatics
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    • v.4 no.1
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    • pp.299-308
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    • 1997
  • In this paper we show that the limit of a convergent in-vertible sequence in the set of invertible elements Inv(A) in a Banach algebra A under a certain conditions is invertible and we investigate some properties of the spectral radius of banach algebra with unit.

Efficient Synthesis of Bibenzyl Derivatives Bearing Pyranyl Moieties: First Total Synthesis of Bauhinol D

  • Park, Byung-Ho;Lee, Yong-Rok;Kim, Sung-Hong
    • Bulletin of the Korean Chemical Society
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    • v.32 no.2
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    • pp.566-570
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    • 2011
  • An efficient and general synthesis of bibenzyl derivatives bearing pyranyl rings was achieved by ethylenediamine diacetate-catalyzed reactions of 3,5-dihydroxybibenzyl with ${\alpha},{\beta}$-unsaturated aldehydes in moderate yields. These reactions provided naturally occurring compounds 1 and 2 in single step reaction. As an application of this methodology, biologically interesting natural bauhinol D (8) was synthesized by a convergent sequence from readily available benzaldehyde and benzyl phosphonate.

First Total Synthesis of Prorepensin with a Bis-Geranylated Chalcone

  • Jung, Eun-Mi;Lee, Yong-Rok
    • Bulletin of the Korean Chemical Society
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    • v.30 no.11
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    • pp.2563-2566
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    • 2009
  • The first total synthesis of naturally occurring prorepensin with a bis-geranylated chalcone has been achieved by a convergent sequence. The key strategy involved in the synthesis of prorepensin was chalcone formation by aldol condensation of the corresponding geranylated acetophenone with geranylated benzaldehyde.

An Iterative Method for Equilibrium and Constrained Convex Minimization Problems

  • Yazdi, Maryam;Shabani, Mohammad Mehdi;Sababe, Saeed Hashemi
    • Kyungpook Mathematical Journal
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    • v.62 no.1
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    • pp.89-106
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    • 2022
  • We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.

CERTAIN ASPECTS OF ROUGH IDEAL STATISTICAL CONVERGENCE ON NEUTROSOPHIC NORMED SPACES

  • Reena Antal;Meenakshi Chawla;Vijay Kumar
    • Korean Journal of Mathematics
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    • v.32 no.1
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    • pp.121-135
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    • 2024
  • In this paper, we have presented rough ideal statistical convergence of sequence on neutrosophic normed spaces as a significant convergence criterion. As neutrosophication can handle partially dependent components, partially independent components and even independent components involved in real-world problems. By examining some properties related to rough ideal convergence in these spaces we have established some equivalent conditions on the set of ideal statistical limit points for rough ideal statistically convergent sequences.

ON CONVERGENCE OF SERIES OF INDEPENDENTS RANDOM VARIABLES

  • Sung, Soo-Hak;Volodin, Andrei-I.
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.4
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    • pp.763-772
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    • 2001
  • The rate of convergence for an almost surely convergent series $S_n={\Sigma^n}_{i-1}X_i$ of independent random variables is studied in this paper. More specifically, when S$_{n}$ converges almost surely to a random variable S, the tail series $T_n{\equiv}$ S - S_{n-1} = {\Sigma^\infty}_{i-n} X_i$ is a well-defined sequence of random variables with T$_{n}$ $\rightarrow$ 0 almost surely. Conditions are provided so that for a given positive sequence {$b_n, n {\geq$ 1}, the limit law sup$_{\kappa}\geqn | T_{\kappa}|/b_n \rightarrow$ 0 holds. This result generalizes a result of Nam and Rosalsky [4].

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On the Almost Certain Rate of Convergence of Series of Independent Random Variables

  • Nam, Eun-Woo;Andrew Rosalsky
    • Journal of the Korean Statistical Society
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    • v.24 no.1
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    • pp.91-109
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    • 1995
  • The rate of convergence to a random variable S for an almost certainly convergent series $S_n = \sum^n_{j=1} X_j$ of independent random variables is studied in this paper. More specifically, when $S_n$ converges to S almost certainly, the tail series $T_n = \sum^{\infty}_{j=n} X_j$ is a well-defined sequence of random variable with $T_n \to 0$ a.c. Various sets of conditions are provided so that for a given numerical sequence $0 < b_n = o(1)$, the tail series strong law of large numbers $b^{-1}_n T_n \to 0$ a.c. holds. Moreover, these results are specialized to the case of the weighted i.i.d. random varialbes. Finally, example are provided and an open problem is posed.

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