Browse > Article
http://dx.doi.org/10.11568/kjm.2019.27.2.343

A FIXED POINT APPROACH TO THE STABILITY OF A QUADRATIC-CUBIC FUNCTIONAL EQUATION  

Lee, Yang-Hi (Department of Mathematics Education Gongju National University of Education)
Publication Information
Korean Journal of Mathematics / v.27, no.2, 2019 , pp. 343-355 More about this Journal
Abstract
In this paper, we investigate the stability of the functional equation $$f(x+ky)-kf(x+y)+kf(x-y)-f(x-ky)-f(ky)+{\frac{k^3+k^2-2k}{2}}f(-y)-{\frac{k^3-k^2-2k}{2}}f(y)=0$$ by using the fixed point theory in the sense of L. $C{\breve{a}}dariu$ and V. Radu.
Keywords
fixed point method; quadratic-cubic functional equation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66.   DOI
2 J. Baker, A general functional equation and its stability, Proc. Natl. Acad. Sci. 133 (6) (2005), 1657-1664.
3 L. Cadariu and V. Radu, Fixed points and the stability of quadratic functional equations, An. Univ. Timisoara Ser. Mat.-Inform. 41 (2003), 25-48.
4 L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach in Iteration Theory, Grazer Mathematische Berichte, Karl-Franzens-Universitaet, Graz, Graz, Austria 346 (2004), 43-52.
5 I.-S. Chang and Y.-S. Jung, Stability of a functional equation deriving from cubic and quadratic functions, J. Math. Anal. Appl. 283 (2003), 491-500.   DOI
6 Y.-J. Cho, M. Eshaghi Gordji, and S. Zolfaghari, Solutions and Stability of Generalized Mixed Type QC Functional Equations in Random Normed Spaces, J. Inequal. Appl. 2010 (2010), Art. ID 403101.
7 S. Czerwik, On the stability of the quadratic mapping in the normed space, Abh. Math. Sem. Hamburg, 62 (1992), 59-64.   DOI
8 J. B. 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.   DOI
9 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. and Appl. 184 (1994), 431-436.   DOI
10 D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA, 27 (1941), 222-224.   DOI
11 C.-J. Lee and Y.-H. Lee, On the stability of a mixed type quadratic and cubic functional equation, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math. 19 (2012), 383-396.
12 Y.-H. Lee and S.-M. Jung, Fuzzy stability of the cubic and quadratic functional equation, Appl. Math. Sci. (Ruse) 10 (2016), 2671-2686.
13 Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.   DOI
14 S.M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1964.
15 W. Towanlong and P. Nakmahachalasint, A Mixed-Type Quadratic and Cubic Functional Equation and Its Stability, Thai J. Math. 8 (4) (2012), 61-71.
16 Z. Wang and W. X. Zhang, Fuzzy stability of quadratic-cubic functional equations, Acta Math. Sin. (Engl. Ser.) 27 (2011), 2191-2204.   DOI