Stability of Pexiderized quadratic functional equation on a set of measure zero

EL-Fassi, Iz-iddine; Chahbi, Abdellatif; Kabbaj, Samir; Park, Choonkil
June 2016
Journal of Nonlinear Sciences & Applications (JNSA);2016, Vol. 9 Issue 6, p4554
Academic Journal
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.


Related Articles

  • 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...

  • Fuzzy Stability of Jensen-Type Quadratic Functional Equations. Sun-Young Jang; Jung Rye Lee; Choonkil Park; Dong Yun Shin // Abstract & Applied Analysis;2009, Special section p1 

    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.

  • Approximation of an additive-quadratic functional equation in RN-spaces. Kenary, Hassan Azadi; Sun-Young Jang; Choonkil Park // Journal of Computational Analysis & Applications;Jan2012, Vol. 14 Issue 1, p1190 

    In this paper, using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation: af (x + y + z/b) + af (x - y + z/b) + af (x + y - z/b) + af (-x + y + z/b) = cf(x) + cf(y) + cf(z) where a, b and c are positive real numbers, in...

  • Stability of an additive-quadratic-quartic functional equation. Kim, Gwang Hui; Lee, Yang-Hi // Demonstratio Mathematica;Jan2020, Vol. 53 Issue 1, p1 

    In this paper, we investigate the stability of an additive-quadratic-quartic functional equation f (x + 2 y) + f (x − 2 y) − 2 f (x + y) − 2 f (− x − y) − 2 f (x − y) − 2 f (y − x) + 4 f (− x) + 2 f (x) − f (2 y) − f...

  • PERIODIC ORBITS OF QUADRATIC POLYNOMIALS. TIMO ERKAMA // Bulletin of the London Mathematical Society;Oct2006, Vol. 38 Issue 5, p804 

    It is known that quadratic polynomials do not have real rational orbits of period four. By using a two-dimensional model for the quadratic family, this result is generalized for complex rational orbits.

  • A fixed point approach to the stability of an AQCQ-functional equation in RN-spaces. Choonkil Park; Dong Yun Shin; Sungjin Lee // Journal of Nonlinear Sciences & Applications (JNSA);2016, Vol. 9 Issue 4, p1787 

    Using the fixed point method, we prove the Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f(-2y) - 4f(y) - 4f(-y) in random normed spaces.

  • Inequalities for certain means in two arguments. Yang, Zhen-Hang; Chu, Yu-Ming // Journal of Inequalities & Applications;9/26/2015, Vol. 2015 Issue 1, p1 

    In this paper, we present the sharp bounds of the ratios $U(a,b)/L_{4}(a,b)$, $P_{2}(a,b)/U(a,b)$, $NS(a,b)/P_{2}(a,b)$ and $B(a,b)/NS(a,b)$ for all $a, b>0$ with $a\neq b$, where $L_{4}(a,b)=[(b^{4}-a^{4})/(4(\log b-\log a))]^{1/4}$, $U(a,b)=(b-a)/[\sqrt{2}\arctan((b-a)/\sqrt{2ab})]$,...

  • The Generalized Hyers--Ulam--Rassias Stability of a Cubic Functional Equation. Najati, Abbas // Turkish Journal of Mathematics;2007, Vol. 31 Issue 4, p395 

    In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a cubic functional equation f(mx + y) + f(mx - y) = mf(x + y) + mf(x - y) + 2(m³ -m)f(x) for a positive integer m ≥ 1.

  • 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...


Read the Article


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

Try another library?
Sign out of this library

Other Topics