• Title/Summary/Keyword: education inequality

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On the analysis and correction of error for the simultaneous inequality with two unknown quantities (미지수가 2개인 연립일차부등식의 문제해결과정에서 발생하는 오류 분석 및 지도방안 연구)

  • Jun, Young-Bae;Roh, Eun-Hwan;Kim, Dae-Eui;Jung, Chan-Sik;Kim, Chang-Su;Kang, Jeong-Gi;Jung, Sang-Tae
    • Communications of Mathematical Education
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    • v.24 no.3
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    • pp.543-562
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    • 2010
  • The purpose of this thesis is to analyze the error happening in the process of solving the simultaneous inequality with two unknown qualities and to propose the correct teaching method. We first introduce a problem about the simultaneous inequality with two unknown qualities. And we will see the solution which a student offers. Finally we propose the correct teaching method by analyzing the error happening in the process of solving the simultaneous inequality with two unknown qualities. The cause of the error are a wrong conception which started with the process of solving the simultaneous equality with two unknown qualities and an insufficient curriculum in connection with the simultaneous inequality with two unknown qualities. Especially we can find out the problem that the students don't look the interrelation between two valuables when they solve the simultaneous inequality with two unknown qualities. Therefore we insist that we must teach students looking the interrelation between two valuables when they solve the simultaneous inequality with two unknown qualities.

FIXED POINTS AND ALTERNATIVE PRINCIPLES

  • Park, Se-Hie;Kim, Hoon-Joo
    • Honam Mathematical Journal
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    • v.34 no.3
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    • pp.439-449
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    • 2012
  • In a recent paper, M. Balaj [B] established an alternative principle. The principle was applied to a matching theorem of Ky Fan type, an analytic alternative, a minimax inequality, and existence of solutions of a vector equilibrium theorem. Based on the first author's fixed point theorems, in the present paper, we obtain generalizations of the main result of Balaj [B] and their applications.

LIMITING BEHAVIOR OF THE MAXIMUM OF THE PARTIAL SUM FOR NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES

  • KIM, HYUN-CHULL
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.3
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    • pp.409-417
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    • 2015
  • In this paper, some $L_p$-convergences and complete convergences of the maximum of the partial sum for negatively superadditive dependent random variables are obtained. The proofs of the results are based on a new Rosenthal type inequality concerning negatively superadditive dependent random variables.

ON ITERATIVE APPROXIMATION OF COMMON FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS WITH APPLICATIONS

  • Kim, Jong Kyu;Qin, Xiaolong;Lim, Won Hee
    • East Asian mathematical journal
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    • v.28 no.5
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    • pp.617-630
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    • 2012
  • In this paper, the problem of iterative approximation of common fixed points of asymptotically nonexpansive is investigated in the framework of Banach spaces. Weak convergence theorems are established. A necessary and sufficient condition for strong convergence is also discussed. As an application of main results, a variational inequality is investigated.

HYPERBOLIC NOTIONS ON A PLANAR GRAPH OF BOUNDED FACE DEGREE

  • OH, BYUNG-GEUN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.4
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    • pp.1305-1319
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    • 2015
  • We study the relations between strong isoperimetric inequalities and Gromov hyperbolicity on planar graphs, and give an alternative proof for the following statement: if a planar graph of bounded face degree satisfies a strong isoperimetric inequality, then it is Gromov hyperbolic. This theorem was formerly proved in the author's paper from 2014 [12] using combinatorial methods, while geometric approach is used in the present paper.

ON THE SUPERCLASSES OF QUASIHYPONORMAL OPERATIORS

  • Cha, Hyung-Koo;Shin, Kyo-Il;Kim, Jae-Hee
    • The Pure and Applied Mathematics
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    • v.7 no.2
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    • pp.79-86
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    • 2000
  • In this paper, we introduce the classes H(p,q,k),K(p;k) of operators determined by the Heinz-Kato-Furuta inequality and Holer-McCarthy inequality. We characterize relationship between p-quasihyponormal, $\kappa$-quasihyponormal and $\kappa$-p-quasihyponormal operators. And it is proved that every operator in K(p;1) for some $0 is paranormal.

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DENSENESS OF TEST FUNCTIONS IN THE SPACE OF EXTENDED FOURIER HYPERFUNCTIONS

  • Kim, Kwang-Whoi
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.4
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    • pp.785-803
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    • 2004
  • We research properties of analytic functions which are exponentially decreasing or increasing. Also we show that the space of test functions is dense in the space of extended Fourier hyper-functions, and that the Fourier transform of the space of extended Fourier hyperfunctions into itself is an isomorphism and Parseval's inequality holds.

THE GENERALIZED HYERS-ULAM STABILITY OF ADDITIVE FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN 2-NORMED SPACE

  • Kim, Chang Il;Park, Se Won
    • Korean Journal of Mathematics
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    • v.22 no.2
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    • pp.339-348
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    • 2014
  • In this paper, we investigate the solution of the following functional inequality $${\parallel}f(x)+f(y)+f(az),\;w{\parallel}{\leq}{\parallel}f(x+y)-f(-az),\;w{\parallel}$$ for some xed non-zero integer a, and prove the generalized Hyers-Ulam stability of it in non-Archimedean 2-normed spaces.

THE SHRINKING PROJECTION METHODS FOR HEMI-RELATIVELY NONEXPANSIVE MAPPINGS, VARIATIONAL INEQUALITIES AND EQUILIBRIUM PROBLEMS

  • Wang, Zi-Ming;Kang, Mi Kwang;Cho, Yeol Je
    • Communications of the Korean Mathematical Society
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    • v.28 no.1
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    • pp.191-207
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    • 2013
  • In this paper, we introduce the shrinking projection method for hemi-relatively nonexpansive mappings to find a common solution of variational inequality problems and equilibrium problems in uniformly convex and uniformly smooth Banach spaces and prove some strong convergence theorems to the common solution by using the proposed method.

THE STABILITY OF A MIXED TYPE FUNCTIONAL INEQUALITY WITH THE FIXED POINT ALTERNATIVE

  • Park, Kyoo-Hong;Jung, Yong-Soo
    • Communications of the Korean Mathematical Society
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    • v.19 no.2
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    • pp.253-266
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    • 2004
  • In this note, by using the fixed point alternative, we investigate the modified Hyers-Ulam-Rassias stability for the following mixed type functional inequality which is either cubic or quadratic: $\parallel$8f(x-3y) + 24f(x+y) + f(8y) -8〔f(x+3y) + 3f(x-y) + 2f(2y)〕$\parallel$$\leq$$\varphi$(x,y).