• Title/Summary/Keyword: Fixed Point Approach,

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STABILITY OF TRIGINTIC FUNCTIONAL EQUATION IN MULTI-BANACH SPACES: FIXED POINT APPROACH

  • Ramdoss, Murali;Aruldass, Antony Raj;Park, Choonkil;Paokanta, Siriluk
    • Korean Journal of Mathematics
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    • v.26 no.4
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    • pp.615-628
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    • 2018
  • In this paper, we introduce the pioneering trigintic functional equation. Moreover, we establish the general solution of the trigintic functional equation and prove the Hyers-Ulam sum and product stabilities of the same equation in multi-Banach spaces by employing the fixed point approach.

A FIXED POINT APPROACH TO STABILITY OF ADDITIVE FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES

  • Kim, Chang Il;Park, Se Won
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.3
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    • pp.453-464
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    • 2016
  • In this paper, we investigate the solution of the following functional inequality $$N(f(x)+f(y)+f(z),t){\geq}N(f(x+y+z),mt)$$ for some fixed real number m with $\frac{1}{3}$ < m ${\leq}$ 1 and using the fixed point method, we prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.

UTILIZING WEAK 𝜓 - 𝜑 CONTRACTION ON FUZZY METRIC SPACES

  • Amrish Handa
    • The Pure and Applied Mathematics
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    • v.30 no.3
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    • pp.309-336
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    • 2023
  • We establish some common fixed point theorems satisfying weak ψ - ϕ contraction on partially ordered non-Archimedean fuzzy metric spaces. By using this results we show the existence of fixed point on the domain of words and apply this approach to deduce the existence of solution for some recurrence equations associated to the analysis of Quicksort algorithms and divide and Conquer algorithms, respectively and also give an example to show the usefulness of our hypothesis. Our results generalize, extend and improve several well-known results of the existing literature in fixed point theory.

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: $$f({\frac{x+y}{2}})+f({\frac{x-y}{2}})=f(x)$$.

FUZZY STABILITY OF A CUBIC-QUARTIC FUNCTIONAL EQUATION: A FIXED POINT APPROACH

  • Jang, Sun-Young;Park, Choon-Kil;Shin, Dong-Yun
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.3
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    • pp.491-503
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    • 2011
  • Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quartic functional equation (0.1) f(2x + y) + f(2x - y) = 3f(x + y) + f(-x - y) + 3f(x - y) + f(y - x) + 18f(x) + 6f(-x) - 3f(y) - 3f(-y) in fuzzy Banach spaces.

A FIXED POINT APPROACH TO THE STABILITY OF QUARTIC LIE ∗-DERIVATIONS

  • Kang, Dongseung;Koh, Heejeong
    • Korean Journal of Mathematics
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    • v.24 no.4
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    • pp.587-600
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    • 2016
  • We obtain the general solution of the functional equation $f(ax+y)-f(x-ay)+{\frac{1}{2}}a(a^2+1)f(x-y)+(a^4-1)f(y)={\frac{1}{2}}a(a^2+1)f(x+y)+(a^4-1)f(x)$ and prove the stability problem of the quartic Lie ${\ast}$-derivation by using a directed method and an alternative fixed point method.