Have a personal or library account? Click to login
Stability of generalized Newton difference equations Cover

References

  1. [1] R. P. Agarwal, B. Xu and W. Zhang, Stability of functional equations in single variable, J. Math. Anal. Appl. 288(2003), 852-869. 10.1016/j.jmaa.2003.09.032
  2. [2] M. Amyari and M. S. Moslehian, Approximately ternary semigroup ho- momorphisms, Lett. Math. Phys. 77(2006), 1-9. 10.1007/s11005-005-0042-6
  3. [3] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2(1950), 64-66. 10.2969/jmsj/00210064
  4. [4] G. L. Forti, Hyers-Ulam stability of functional equations in several vari- ables, Aequationes Math. 50(1995), 143-190. 10.1007/BF01831117
  5. [5] P. G˘avruta, A generalization of the Hyers-Ulam-Rassias stability of ap- proximately additive mappings, J. Math. Anal. Appl. 184(1994), 431-436. 10.1006/jmaa.1994.1211
  6. [6] K. J. Heuvers, D. S. Moak and B. Boursaw, The functional equation of the square root spiral, In Functional Equations and Inequalities, (Edited by Th. M. Rassias), Kluwer, 2000, pp. 111-117. 10.1007/978-94-011-4341-7_10
  7. [7] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27(1941), 222-224. 10.1073/pnas.27.4.222
  8. [8] S.-M. Jung, Hyers-Ulam-Rassias stability of functional equations, Dynam. Systems Appl. 6(1997), 541-566.
  9. [9] S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer, New York, 2011. 10.1007/978-1-4419-9637-4
  10. [10] S.-M. Jung and P. K. Sahoo, Hyers-Ulam stability of the quadratic equa- tion of Pexider type, J. Korean Math. Soc. 38(2001), 645-656.
  11. [11] S.-M. Jung and P. K. Sahoo, Stability of a functional equation for square root spirals, Appl. Math. Lett. 15(2002), 435-438. 10.1016/S0893-9659(01)00155-0
  12. [12] S.-M. Jung and J. M. Rassias, Stability of general Newton functional equations for logarithmic spirals, Advances in Difference Equations, Vol- ume 2008, Article ID 143053, 5 pages. 10.1155/2008/143053
  13. [13] G. H. Kim, B. Xu and W. Zhang, Notes on stability of the generalized gamma functional equation, Internat. J. Math. Math. Sci. 32(2002), 57-63. 10.1155/S0161171202112129
  14. [14] G. H. Kim, On the Hyers-Ulam-Rassias stability of functional equations in n-variables, J. Math. Anal. Appl. 299(2004), 375-391. 10.1016/j.jmaa.2004.02.064
  15. [15] M. Kuczma, B. Choczewski and R. Ger, Iterative Functional Equations, Encyclopedia Math. Appl. Vol. 32, Cambridge Univ. Press, 1990. 10.1017/CBO9781139086639
  16. [16] M. Mirzavaziri and M. S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. 37(3)(2006), 361-376. 10.1007/s00574-006-0016-z
  17. [17] A. K. Mirmostafaee and M. S. Moslehian, Fuzzy versions of Hyers-Ulam- Rassias theorem, Fuzzy Sets and Systems 159(2008), 720-729. 10.1016/j.fss.2007.09.016
  18. [18] M. S. Moslehian, K. Nikodem and D. Popa, Asymptotic aspect of the quadratic functional equation in multi-normed spaces, J. Math. Anal. Appl. 355(2009), 717-724. 10.1016/j.jmaa.2009.02.017
  19. [19] A. Najati and M. B. Moghimi, Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spaces, J. Math. Anal. Appl. 337(2008), 399-415. 10.1016/j.jmaa.2007.03.104
  20. [20] K. Nikodem, The stability of the Pexider equations, Ann. Math. Sil. 5(1991), 91-93.
  21. [21] Ch. Park, Hyers-Ulam-Rassias stability of homomorphisms in quasi- Banach algebras, Bull. Sci. Math. 132(2008), 87-96. 10.1016/j.bulsci.2006.07.004
  22. [22] T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300. 10.1090/S0002-9939-1978-0507327-1
  23. [23] T. Trif, On the stability of a general gamma-type functional equation, Publ. Math. Debrecen 60(2002), 47-61 10.5486/PMD.2002.2522
  24. [24] S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science Edi- tions, Wiley, New York, 1964.
  25. [25] Z. Wang, X. Chen and B. Xu, Generalization of functional equation for the square root spiral, Appl. Math. Comput. 182(2006), 1355-1360.
DOI: https://doi.org/10.2478/v10309-012-0031-6 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 459 - 466
Published on: May 17, 2013
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year

© 2013 Zhihua Wang, Yong-Guo Shi, published by Ovidius University of Constanta
This work is licensed under the Creative Commons License.