• Title, Summary, Keyword: cubic function

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ON STABILITY OF THE ORTHOGONALLY CUBIC TYPE FUNCTIONAL EQUATION

  • Chang, Ick-Soon
    • Journal of the Chungcheong Mathematical Society
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    • v.19 no.3
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    • pp.275-281
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    • 2006
  • In this article, we establish the stability of the orthogonally cubic type functional equation 2f(x + 2y) + 2f(x - 2y) + 2f(2x)+7[f(x)+f(-x)] = 4f(x)+8[f(x+y)+f(x-y)], $x{\bot}y$ in which ${\bot}$ is the orthogonality in the sense in the R$\ddot{a}$tz.

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Synthesis of Optimum CAM Curve by Cubic Spline (Cubic Spline을 사용한 최적 캠곡선의 합성)

  • 손태영;양민양
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.5
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    • pp.1168-1175
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    • 1995
  • The application of cubic spline is presented for basic curve (DRD motion) of cam motion. The purpose of this paper is to achieve better dynamic characteristics than general cam curves. A cubic spline is a piecewise function that is continuous in displacement, velocity and acceleration. The best cam curve is obtained by changing the weights of the object function. So the method can be used to any machine system case by case. For the proposed object function, the result has improved all characteristics such as velocity, acceleration and jerk compared with that of the modified sine curve.

General Formulas for Explicit Evaluations of Ramanujan's Cubic Continued Fraction

  • Naika, Megadahalli Sidda Naika Mahadeva;Maheshkumar, Mugur Chinna Swamy;Bairy, Kurady Sushan
    • Kyungpook Mathematical Journal
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    • v.49 no.3
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    • pp.435-450
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    • 2009
  • On page 366 of his lost notebook [15], Ramanujan recorded a cubic continued fraction and several theorems analogous to Rogers-Ramanujan's continued fractions. In this paper, we derive several general formulas for explicit evaluations of Ramanujan's cubic continued fraction, several reciprocity theorems, two formulas connecting V (q) and V ($q^3$) and also establish some explicit evaluations using the values of remarkable product of theta-function.

FUZZY ALMOST q-CUBIC FUNCTIONAL EQATIONS

  • Kim, ChangIl
    • Journal of the Chungcheong Mathematical Society
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    • v.30 no.2
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    • pp.239-249
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    • 2017
  • In this paper, we approximate a fuzzy almost cubic function by a cubic function in a fuzzy sense. Indeed, we investigate solutions of the following cubic functional equation $$3f(kx+y)+3f(kx-y)-kf(x+2y)-2kf(x-y)-3k(2k^2-1)f(x)+6kf(y)=0$$. and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.