• Title, Summary, Keyword: Jensen type equation

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STABILITY OF A JENSEN TYPE FUNCTIONAL EQUATION

  • Lee, Sang Han
    • Journal of the Chungcheong Mathematical Society
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    • v.14 no.1
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    • pp.73-83
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    • 2001
  • In this paper, we solve a Jensen type functional equation and prove the stability of the Jensen type functional equation.

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ON THE STABILITY OF A JENSEN TYPE FUNCTIONAL EQUATION ON GROUPS

  • FAIZIEV VALERH A.;SAHOO PRASANNA K.
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.757-776
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    • 2005
  • In this paper we establish the stability of a Jensen type functional equation, namely f(xy) - f($xy^{-1}$) = 2f(y), on some classes of groups. We prove that any group A can be embedded into some group G such that the Jensen type functional equation is stable on G. We also prove that the Jensen type functional equation is stable on any metabelian group, GL(n, $\mathbb{C}$), SL(n, $\mathbb{C}$), and T(n, $\mathbb{C}$).

STABILITY OF PEXIDERIZED JENSEN AND JENSEN TYPE FUNCTIONAL EQUATIONS ON RESTRICTED DOMAINS

  • Choi, Chang-Kwon
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.801-813
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    • 2019
  • In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of pexiderized Jensen functional equation $$2f(\frac{x+y}{2})-g(x)-h(y)=0$$ and pexiderized Jensen type functional equations $$f(x+y)+g(x-y)-2h(x)=0,\\f(x+y)-g(x-y)-2h(y)=0$$ on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.

STABILITY OF THE JENSEN TYPE FUNCTIONAL EQUATION IN BANACH ALGEBRAS: A FIXED POINT APPROACH

  • Park, Choonkil;Park, Won Gil;Lee, Jung Rye;Rassias, Themistocles M.
    • Korean Journal of Mathematics
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    • v.19 no.2
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    • pp.149-161
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    • 2011
  • Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the following Jensen type functional equation: $$f({\frac{x+y}{2}})+f({\frac{x-y}{2}})=f(x)$$.

STABILITY OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION WITH JENSEN TYPE

  • LEE, YOUNG-WHAN
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.57-73
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    • 2005
  • In this paper we solve a generalized quadratic Jensen type functional equation $m^2 f (\frac{x+y+z}{m}) + f(x) + f(y) + f(z) =n^2 [f(\frac{x+y}{n}) +f(\frac{y+z}{n}) +f(\frac{z+x}{n})]$ and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.

STABILITY OF FUNCTIONAL EQUATIONS WITH RESPECT TO BOUNDED DISTRIBUTIONS

  • Chung, Jae-Young
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.3
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    • pp.361-370
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    • 2008
  • We consider the Hyers-Ulam type stability of the Cauchy, Jensen, Pexider, Pexider-Jensen differences: $$(0.1){\hspace{55}}C(u):=u{\circ}A-u{\circ}P_1-u{\circ}P_2,\\(0.2){\hspace{55}}J(u):=2u{\circ}\frac{A}{2}-u{\circ}P_1-u{\circ}P_2,\\(0.3){\hspace{18}}P(u,v,w):=u{\circ}A-v{\circ}P_1-w{\circ}P_2,\\(0.4)\;JP(u,v,w):=2u{\circ}\frac{A}{2}-v{\circ}P_1-w{\circ}P_2$$, with respect to bounded distributions.

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APPROXIMATELY ADDITIVE MAPPINGS IN NON-ARCHIMEDEAN NORMED SPACES

  • Mirmostafaee, Alireza Kamel
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.387-400
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    • 2009
  • We establish a new strategy to study the Hyers-Ulam-Rassias stability of the Cauchy and Jensen equations in non-Archimedean normed spaces. We will also show that under some restrictions, every function which satisfies certain inequalities can be approximated by an additive mapping in non-Archimedean normed spaces. Some applications of our results will be exhibited. In particular, we will see that some results about stability and additive mappings in real normed spaces are not valid in non-Archimedean normed spaces.