Fuzzy Stability of Jensen-Type Quadratic Functional Equations

Sun-Young Jang; Jung Rye Lee; Choonkil Park; Dong Yun Shin
January 2009
Abstract & Applied Analysis;2009, Special section p1
Academic Journal
We prove the generalized Hyers-Ulam stability of the following quadratic functional equations 2f((x + y)/2) + 2f((x - y)/2) = f(x) + f(y) and f(ax + ay) = (ax - ay) = 2a2f(x) + 2a2f(y) in fuzzy Banach spaces for a nonzero real number a with a≠ ± 1/2.


Related Articles

  • Fuzzy Stability of Quadratic Functional Equations. Jung Rye Lee; Sun-Young Jang; Choonkil Park; Dong Yun Shin // Advances in Difference Equations;2010, Special section p1 

    No abstract available.

  • Stability of Pexiderized quadratic functional equation on a set of measure zero. EL-Fassi, Iz-iddine; Chahbi, Abdellatif; Kabbaj, Samir; Park, Choonkil // Journal of Nonlinear Sciences & Applications (JNSA);2016, Vol. 9 Issue 6, p4554 

    Let R be the set of real numbers and Y a Banach space. We prove the Hyers-Ulam stability theorem when f; h : R → Y satisfy the following Pexider quadratic inequality ‖f(x + y) + f(x - y) - 2f(x) - 2h(y)‖ ≤ ε, in a set Ω ⊂ R2 of Lebesgue measure m(Ω) = 0.

  • On the Generalized Hyers-Ulam-Rassias Stability for a Functional Equation of Two Types in p-Banach Spaces. Kyoo-Hong Park; Yong-Soo Jung // Kyungpook Mathematical Journal;2008, Vol. 48 Issue 1, p45 

    We investigate the generalized Hyers-Ulam-Rassias stability in p-Banach spaces for the following functional equation which is two types, that is, either cubic or quadratic: 2f(x + 3y) + 6f(x - y) + 12f(2y) = 2f(x - 3y) + 6f(x + y) + 3f(4y). The concept of Hyers-Ulam-Rassias stability originated...

  • ON THE GENERALIZED ULAM-HYERS STABILITY OF AN AQ-MIXED TYPE FUNCTIONAL EQUATION WITH COUNTEREXAMPLES. Arunkumar, M.; Rassias, John M. // Far East Journal of Mathematical Sciences;Dec2012, Vol. 71 Issue 2, p279 

    In this paper, the authors establish the generalized Ulam-Hyers stability of an additive and quadratic (AQ)-mixed type functional equation f (x + y) + f (x − y) = 2 f (x) + f (y) + f (−y) in Banach spaces. Various counterexamples for nonstability cases are also provided.

  • Solution and stability of mixed type functional equation in p -- Banach spaces. Ravi, K.; Narasimman, P. // Journal of Advanced Research in Pure Mathematics;2011, Vol. 3 Issue 2, p7 

    In this paper, the authors investigate the general solution and generalized Hyers - Ulam - Rassias stability of a mixed type additive and quadratic functional equation f(2x - y) + f(2y - z) + f(2z - x) + f(x + y + z) - f(x - y + z) - f(x + y - z) - f(x - y - z) - 2[f(2x) - 4f(x)] = 3f(x) + 3f(y)...

  • On the stability of a mixed functional equation deriving from additive, quadratic and cubic mappings. Wang, Li; Xu, Kun; Liu, Qiu // Acta Mathematica Sinica;Jun2014, Vol. 30 Issue 6, p1033 

    In this paper, we investigate the general solution and the Hyers-Ulam stability of the following mixed functional equation deriving from additive, quadratic and cubic mappings on Banach spaces.

  • Stability of a Jensen type quadratic-additive functional equation under the approximately conditions. Lee, Young-Su; Jeong, Yujin; Ha, Hyemin // Advances in Difference Equations;9/16/2015, Vol. 2015 Issue 1, p1 

    We prove the Hyers-Ulam-Rassias stability of the Jensen type quadratic and additive functional equation $9f ( \frac{x+y+z}{3} ) + 4 [ f (\frac{x-y}{2} ) + f (\frac{y-z}{2} ) + f (\frac{z-x}{2} ) ] = 3 [ f(x)+f(y)+f(z) ]$ under the approximately conditions such as even, odd, quadratic, and...

  • Orthogonal stability of a quadratic functional inequality: a fixed point approach. Farhadabadi, Shahrokh; Choonkil Park // Journal of Computational Analysis & Applications;Jan2021, Vol. 29 Issue 1, p140 

    Let f : X → Y be a mapping from an orthogonality space (X, ⊥) into a real Banach space (Y, ∥ · ∥). Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally quadratic functional inequality...

  • QUADRATIC FUNCTIONAL EQUATION AND ITS STABILITY IN FELBIN'S TYPE SPACES. Ravi, K.; Sabarinathan, S. // Far East Journal of Mathematical Sciences;Dec2015, Vol. 98 Issue 8, p977 

    In this paper, we introduce a new quadratic functional equation, obtain the general solution and investigate the Hyers-Ulam stability, Hyers-Ulam-Rassias stability and generalized Hyers-Ulam-Rassias stability for the quadratic functional equations in Felbin's type fuzzy normed linear spaces. A...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics