JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A FIXED POINT APPROACH TO THE STABILITY OF QUADRATIC FUNCTIONAL EQUATION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A FIXED POINT APPROACH TO THE STABILITY OF QUADRATIC FUNCTIONAL EQUATION
Jung, Soon-Mo; Kim, Tae-Soo; Lee, Ki-Suk;
  PDF(new window)
 Abstract
[ ] and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of and Radu to prove the Hyers-Ulam-Rassias stability of the quadratic functional equation for a large class of functions from a vector space into a complete space.
 Keywords
Hyers-Ulam-Rassias stability;quadratic functional equation;fixed point method;
 Language
English
 Cited by
1.
A Fixed Point Approach to the Stability of Quadratic Equations in Quasi Normed Spaces,;

Kyungpook mathematical journal, 2009. vol.49. 4, pp.691-700 crossref(new window)
2.
STABILITY OF THE MONOMIAL FUNCTIONAL EQUATION IN QUASI NORMED SPACES,;

대한수학회보, 2010. vol.47. 4, pp.777-785 crossref(new window)
1.
A Fixed Point Approach to the Stability of Quadratic Equations in Quasi Normed Spaces, Kyungpook mathematical journal, 2009, 49, 4, 691  crossref(new windwow)
2.
On the $$\beta $$ β -Ulam–Hyers–Rassias stability of nonautonomous impulsive evolution equations, Journal of Applied Mathematics and Computing, 2015, 48, 1-2, 461  crossref(new windwow)
3.
Existence and stability of Stieltjes quadratic functional integral equations, Journal of Applied Mathematics and Computing, 2017, 53, 1-2, 183  crossref(new windwow)
4.
A class of nonlinear differential equations with fractional integrable impulses, Communications in Nonlinear Science and Numerical Simulation, 2014, 19, 9, 3001  crossref(new windwow)
5.
A Fixed Point Approach to the Stability of ann-Dimensional Mixed-Type Additive and Quadratic Functional Equation, Abstract and Applied Analysis, 2012, 2012, 1  crossref(new windwow)
6.
STABILITY OF THE MONOMIAL FUNCTIONAL EQUATION IN QUASI NORMED SPACES, Bulletin of the Korean Mathematical Society, 2010, 47, 4, 777  crossref(new windwow)
7.
A functional equation having monomials as solutions, Applied Mathematics and Computation, 2010, 216, 1, 87  crossref(new windwow)
8.
Stability of a Bi-Additive Functional Equation in Banach Modules Over aC⋆-Algebra, Discrete Dynamics in Nature and Society, 2012, 2012, 1  crossref(new windwow)
9.
Normed spaces equivalent to inner product spaces and stability of functional equations, Aequationes mathematicae, 2014, 87, 1-2, 147  crossref(new windwow)
10.
A HYPERSTABILITY RESULT FOR THE CAUCHY EQUATION, Bulletin of the Australian Mathematical Society, 2014, 89, 01, 33  crossref(new windwow)
11.
Existence and approximation of solutions of fractional order iterative differential equations, Open Physics, 2013, 11, 10  crossref(new windwow)
12.
Existence and β-Ulam-Hyers stability for a class of fractional differential equations with non-instantaneous impulses, Advances in Difference Equations, 2015, 2015, 1  crossref(new windwow)
13.
Stability for a family of equations generalizing the equation of p-Wright affine functions, Applied Mathematics and Computation, 2016, 276, 158  crossref(new windwow)
14.
Analysis of fractional order differential coupled systems, Mathematical Methods in the Applied Sciences, 2015, 38, 15, 3322  crossref(new windwow)
15.
Hyperstability of the Cauchy equation on restricted domains, Acta Mathematica Hungarica, 2013, 141, 1-2, 58  crossref(new windwow)
16.
On the generalized Hyers–Ulam stability of multi-quadratic mappings, Computers & Mathematics with Applications, 2011, 62, 9, 3418  crossref(new windwow)
17.
Stability of ann-Dimensional Mixed-Type Additive and Quadratic Functional Equation in Random Normed Spaces, Journal of Applied Mathematics, 2012, 2012, 1  crossref(new windwow)
18.
On a new class of impulsive fractional differential equations, Applied Mathematics and Computation, 2014, 242, 649  crossref(new windwow)
 References
1.
L. Cadariu and V. Radu, Fixed points and the stability of Jensen's functional equation, JIPAM. J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Art. 4, 7 pp

2.
L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber. 346 (2004), 43-52

3.
P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), no. 1-2, 76-86 crossref(new window)

4.
S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64 crossref(new window)

5.
J. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309 crossref(new window)

6.
G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143-190 crossref(new window)

7.
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224

8.
D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel/Boston, 1998

9.
D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153 crossref(new window)

10.
S.-M. Jung, Hyers-Ulam-Rassias stability of functional equations, Dynam. Sys tems Appl. 6 (1997), no. 4, 541-566

11.
S.-M. Jung, On the Hyers-Ulam stability of the functional equations that have the quadratic property, J. Math. Anal. Appl. 222 (1998), no. 1, 126-137 crossref(new window)

12.
S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001

13.
V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), no. 1, 91-96

14.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300

15.
Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), no. 1, 23-130 crossref(new window)

16.
F. Skof, Proprieta locali e approssimazione di operatori , Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129 crossref(new window)

17.
S. M. Ulam, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience Publisher, New York, 1960