대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제28권2호
  • /
  • Pages.269-283
  • /
  • 2013
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A FIXED POINT APPROACH TO THE STABILITY OF THE GENERALIZED POLYNOMIAL FUNCTIONAL EQUATION OF DEGREE 2

  • Jin, Sun-Sook (Department of Mathematics Education Gongju National University of Education) ;
  • Lee, Yang-Hi (Department of Mathematics Education Gongju National University of Education)
  • 투고 : 2011.04.14
  • 발행 : 2013.04.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we investigate a stability of the functional equation $$\sum^3_{i=0}_3C_i(-1)^{3-i}f(ix+y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.

키워드

참고문헌

  1. T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66. https://doi.org/10.2969/jmsj/00210064
  2. L. Cadariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Art. 4, 7 pp.
  3. L. Cadariu and V. Radu, Fixed points and the stability of quadratic functional equations, An. Univ. Timisoara Ser. Mat.-Inform. 41 (2003), no. 1, 25-48.
  4. 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. https://doi.org/10.1090/S0002-9904-1968-11933-0
  5. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436. https://doi.org/10.1006/jmaa.1994.1211
  6. D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  7. S. S. Jin and Y. H. Lee, A fixed point approach to the stability of the Cauchy additive and quadratic type functional equation, J. Appl. Math. 2011 (2011), Article ID 817079, 16 pages.
  8. S. S. Jin and Y. H. Lee, A fixed point approach to the stability of the quadratic-additive functional equation, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 18 (2011), no. 4, 313-328. https://doi.org/10.7468/jksmeb.2011.18.4.313
  9. S. S. Jin and Y. H. Lee, A fixed point approach to the stability of the mixed type functional equation, Honam Math. J. 34 (2012), no. 1, 19-34. https://doi.org/10.5831/HMJ.2012.34.1.19
  10. K.-W. Jun and Y.-H. Lee, A generalization of the Hyers-Ulam-Rassias stability of the Pexiderized quadratic equations. II, Kyungpook Math. J. 47 (2007), no. 1, 91-103.
  11. K.-W. Jun, Y.-H. Lee, and J.-R. Lee, On the stability of a new Pexider type functional equation, J. Inequal. Appl. 2008 (2008), ID 816963, 22 pages. https://doi.org/10.1155/2008/816963
  12. G.-H. Kim, On the stability of functional equations with square-symmetric operation, Math. Inequal. Appl. 4 (2001), no. 2, 257-266.
  13. H.-M. Kim, On the stability problem for a mixed type of quartic and quadratic functional equation, J. Math. Anal. Appl. 324 (2006), no. 1, 358-372. https://doi.org/10.1016/j.jmaa.2005.11.053
  14. Y.-H. Lee, On the Hyers-Ulam-Rassias stability of the generalized polynomial function of degree 2, J. Chuncheong Math. Soc. 22 (2009), no. 2, 201-209.
  15. Y.-H. Lee, On the stability of the monomial functional equation, Bull. Korean Math. Soc. 45 (2008), no. 2, 397-403. https://doi.org/10.4134/BKMS.2008.45.2.397
  16. Y. H. Lee and K. W. Jun, A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation, J. Math. Anal. Appl. 238 (1999), no. 1, 305-315. https://doi.org/10.1006/jmaa.1999.6546
  17. Y. H. Lee and K. W. Jun, A generalization of the Hyers-Ulam-Rassias stability of the Pexider equation, J. Math. Anal. Appl. 246 (2000), no. 2, 627-638. https://doi.org/10.1006/jmaa.2000.6832
  18. Y. H. Lee and K. W. Jun, A note on the Hyers-Ulam-Rassias stability of Pexider equation, J. Korean Math. Soc. 37 (2000), no. 1, 111-124.
  19. Y. H. Lee and K. W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc. 128 (2000), no. 5, 1361-1369. https://doi.org/10.1090/S0002-9939-99-05156-4
  20. Y. H. Lee and S. M. Jung, A fixed point approach to the stability of an n-dimensional mixed-type additive and quadratic functional equation, Abstr. Appl. Anal. 2012 (2012), Article ID 482936, 14 pages.
  21. Y. H. Lee and S. M. Jung, A fixed point approach to the generalized Hyer-Ulam stability of a mixed type functional equation, Int. J. Pure Appl. Math. 81 (2012), no. 2, 359-375.
  22. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  23. I. A. Rus, Principles and Applications of Fixed Point Theory, Ed. Dacia, Cluj-Napoca, 1979.
  24. S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.

피인용 문헌

  1. STABILITY OF A GENERALIZED POLYNOMIAL FUNCTIONAL EQUATION OF DEGREE 2 IN NON-ARCHIMEDEAN NORMED SPACES vol.26, pp.4, 2013, https://doi.org/10.14403/jcms.2013.26.4.887