• 제목/요약/키워드: generalized Ulam-Hyers stability

검색결과 164건 처리시간 0.019초

FUZZY STABILITY OF QUADRATIC-CUBIC FUNCTIONAL EQUATIONS

  • Kim, Chang Il;Yun, Yong Sik
    • East Asian mathematical journal
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    • 제32권3호
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    • pp.413-423
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    • 2016
  • In this paper, we consider the functional equation f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 3f(y) + 3f(-y) = 0 and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy Banach space. The usual method to obtain the stability for mixed type functional equation is to split the cases according to whether the involving mappings are odd or even. In this paper, we show that the stability of a quadratic-cubic mapping can be obtained without distinguishing the two cases.

ON THE FUZZY STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS

  • Lee, Jung-Rye;Jang, Sun-Young;Shin, Dong-Yun
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제17권1호
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    • pp.65-80
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    • 2010
  • In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = $2a^2 f(x)\;+\;2b^2f(y)$ for nonzero real numbers a, b with $a\;{\neq}\;{\pm}1$.

STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS IN RANDOM NORMED SPACES

  • Schin, Seung Won;Ki, DoHyeong;Chang, JaeWon;Kim, Min June;Park, Choonkil
    • Korean Journal of Mathematics
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    • 제18권4호
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    • pp.395-407
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    • 2010
  • In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations $$cf\(\sum_{i=1}^{n}x_i\)+\sum_{j=2}^{n}f\(\sum_{i=1}^{n}x_i-(n+c-1)x_j\)\\=(n+c-1)\(f(x_1)+c\sum_{i=2}^{n}f(x_i)+\sum_{i<j,j=3}^{n}\(\sum_{i=2}^{n-1}f(x_i-x_j\)\),\\Q\(\sum_{i=1}^{n}d_ix_i\)+\sum_{1{\leq}i<j{\leq}n}d_id_jQ(x_i-x_j)=\(\sum_{i=1}^{n}d_i\)\(\sum_{i=1}^{n}d_iQ(x_i)\)$$ in random normed spaces.

ON SOLUTIONS AND STABILITY OF A GENERALIZED QUADRATIC EQUATION ON NON-ARCHIMEDEAN NORMED SPACES

  • Janfada, Mohammad;Shourvarzi, Rahele
    • Journal of applied mathematics & informatics
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    • 제30권5_6호
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    • pp.829-845
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    • 2012
  • In this paper we study general solutions and generalized Hyers-Ulam-Rassias stability of the following function equation $$f(x-\sum^{k}_{i=1}x_i)+(k-1)f(x)+(k-1)\sum^{k}_{i=1}(x_i)=f(x-x_1)+\sum^{k}_{i=2}f(x_i-x)+\sum^{k}_{i=1}\sum^{k}_{j=1,j > i}f(x_i+x_j)$$. for $k{\geq}2$, on non-Archimedean Banach spaces. It will be proved that this equation is equivalent to the so-called quadratic functional equation.

JORDAN *-HOMOMORPHISMS BETWEEN UNITAL C*-ALGEBRAS

  • Gordji, Madjid Eshaghi;Ghobadipour, Norooz;Park, Choon-Kil
    • 대한수학회논문집
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    • 제27권1호
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    • pp.149-158
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    • 2012
  • In this paper, we prove the superstability and the generalized Hyers-Ulam stability of Jordan *-homomorphisms between unital $C^*$-algebras associated with the following functional equation$$f(\frac{-x+y}{3})+f(\frac{x-3z}{c})+f(\frac{3x-y+3z}{3})=f(x)$$. Morever, we investigate Jordan *-homomorphisms between unital $C^*$-algebras associated with the following functional inequality $${\parallel}f(\frac{-x+y}{3})+f(\frac{x-3z}{3})+f(\frac{3x-y+3z}{3}){\parallel}\leq{\parallel}f(x)\parallel$$.

GENERALIZED JENSEN'S FUNCTIONAL EQUATIONS AND APPROXIMATE ALGEBRA HOMOMORPHISMS

  • Bae, Jae-Hyeong;Park, Won-Gil
    • 대한수학회보
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    • 제39권3호
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    • pp.401-410
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    • 2002
  • We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with generalized Jensen's functional equations in Banach algebras.

ON STABILITY OF THE EQUATION - g(x+p,y+q) = ${\varphi}(x,y)g(x,y)$

  • Shin, Dong-Soo;Kim, Gwang-Hui
    • Journal of applied mathematics & informatics
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    • 제7권3호
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    • pp.1017-1027
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    • 2000
  • On the positive real number, we obtain the Hyers-Ulam stability and a stability in the sense of R. Ger for the generalized beta function g(x+p,y+q) = ${\varphi}(x,y)g(x,y)$ in the following settings: $$\mid$g(x+p,y+q)-{\varphi}(x,y)g(x,y)$\mid${\leq}{\delta}$ and $$\mid$\frac{g(x+p,y+q)}{\varphi(x,y)g(x,y)}-1$\mid${\leq}{\psi}(x,y). As a consequence we obtain stability theorems for the gamma functional equation and the beta functional equation.