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NAN-RN Approximately Generalized Additive Functional Equations

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 134))

Abstract

The authors have studied the generalized Hyers-Ulam-Rassias stability of approximately generalized additive functional equations.

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References

  1. L.M. Arriola, W.A. Beyer, Stability of the Cauchy functional equation over p-adic fields. Real Anal. Exchange 31, 125–132 (2005/06)

    Article  MathSciNet  Google Scholar 

  2. H. Azadi Kenary, Stability of a Pexiderial functional equation in random normed spaces. Rend. Circ. Mat. Palermo 60, 59–68 (2011). https://doi.org/10.1007/s12215-011-0027-5

    Article  MathSciNet  Google Scholar 

  3. H. Azadi Kenary, C. Park, Direct and fixed point methods approach to the generalized Hyers–Ulam stability for a functional equation having monomials as solutions. Iran. J. Sci. Technol. Trans. A A4, 301–307 (2011)

    MathSciNet  Google Scholar 

  4. H. Azadi Kenary, J.R. Lee, C. Park, Non-Archimedean stability of an AQQ functional equation. J. Comput. Anal. Appl. 14(2), 211–227 (2012)

    MathSciNet  MATH  Google Scholar 

  5. H. Azadi Kenary, H. Rezaei, S. Talebzadeh, S.J. Lee, Stabilities of cubic mappings in various normed spaces: direct and fixed point methods. J. Appl. Math. 2012, Article ID 546819, 28 pp. (2012)

    Google Scholar 

  6. P.W. Cholewa, Remarks on the stability of functional equations. Aequationes Math. 27, 76–86 (1984)

    Article  MathSciNet  Google Scholar 

  7. S. Czerwik, Functional Equations and Inequalities in Several Variables (World Scientific, River Edge, 2002)

    Book  Google Scholar 

  8. D. Deses, On the representation of non-Archimedean objects. Topol. Appl. 153, 774–785 (2005)

    Article  MathSciNet  Google Scholar 

  9. M. Eshaghi Gordji, M. Bavand Savadkouhi, Stability of mixed type cubic and quartic functional equations in random normed spaces. J. Inequal. Appl. 2009, Article ID 527462, 9 pp. (2009)

    Google Scholar 

  10. M. Eshaghi Gordji, M.B. Savadkouhi, Stability of cubic and quartic functional equations in non-Archimedean spaces. Acta Applicandae Math. 110, 1321–1329 (2010)

    Article  MathSciNet  Google Scholar 

  11. M. Eshaghi Gordji, M. Bavand Savadkouhi, C. Park, Quadratic-quartic functional equations in RN-spaces. J. Inequal. Appl. 2009, Article ID 868423, 14 pp. (2009)

    Google Scholar 

  12. M. Eshaghi Gordji, S. Zolfaghari, J.M. Rassias, M.B. Savadkouhi, Solution and stability of a mixed type cubic and quartic functional equation in quasi-Banach spaces. Abstr. Appl. Anal. 2009, Article ID 417473, 14 pp. (2009)

    Google Scholar 

  13. P. Gǎvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184, 431–436 (1994)

    Google Scholar 

  14. K. Hensel, Ubereine news Begrundung der Theorie der algebraischen Zahlen. Jahresber. Deutsch. Math. Verein 6, 83–88 (1897)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  16. S.M. Jung, Hyers-Ulam-Rassias stability of Jensen’s equation and its application. Proc. Am. Math. Soc. 126, 3137–3143 (1998)

    Article  MathSciNet  Google Scholar 

  17. S.-M. Jung, M.Th. Rassias, A linear functional equation of third order associated to the Fibonacci numbers. Abstr. Appl. Anal. 2014, Article ID 137468 (2014)

    Article  MathSciNet  Google Scholar 

  18. S.-M. Jung, D. Popa, M.Th. Rassias, On the stability of the linear functional equation in a single variable on complete metric groups. J. Glob. Optim. 59, 165–171 (2014)

    Article  MathSciNet  Google Scholar 

  19. S.-M. Jung, M.Th. Rassias, C. Mortici, On a functional equation of trigonometric type. Appl. Math. Comput. 252, 294–303 (2015)

    MathSciNet  MATH  Google Scholar 

  20. A.K. Katsaras, A. Beoyiannis, Tensor products of non-Archimedean weighted spaces of continuous functions. Georgian Math. J. 6, 33–44 (1999)

    Article  MathSciNet  Google Scholar 

  21. A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, vol. 427. Mathematics and Its Applications (Kluwer Academic Publishers, Dordrecht, 1997)

    Book  Google Scholar 

  22. D. Mihet, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces. J. Math. Anal. Appl. 343, 567–572 (2008)

    Article  MathSciNet  Google Scholar 

  23. A.K. Mirmostafaee, Approximately additive mappings in non-Archimedean normed spaces. Bull. Korean Math. Soc. 46, 387–400 (2009)

    Article  MathSciNet  Google Scholar 

  24. C. Mortici, M.Th. Rassias, S.-M. Jung, On the stability of a functional equation associated with the Fibonacci numbers. Abstr. Appl. Anal. 2014, Article ID 546046, 6 pp. (2014)

    Google Scholar 

  25. M.S. Moslehian, Th.M. Rassias, Stability of functional equations in non-Archimedean spaces. Appl. Anal. Discrete Math. 1, 325–334 (2007)

    Article  MathSciNet  Google Scholar 

  26. P.J. Nyikos, On some non-Archimedean spaces of Alexandrof and Urysohn. Topol. Appl. 91, 1–23 (1999)

    Article  MathSciNet  Google Scholar 

  27. C. Park, Generalized Hyers-Ulam-Rassias stability of n-sesquilinear-quadratic mappings on Banach modules over C -algebras. J. Comput. Appl. Math. 180, 279–291 (2005)

    Article  MathSciNet  Google Scholar 

  28. C. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras. Fixed Point Theory Appl. 2007, Article ID 50175 (2007)

    Article  MathSciNet  Google Scholar 

  29. C. Park, Generalized Hyers-Ulam-Rassias stability of quadratic functional equations: a fixed point approach. Fixed Point Theory Appl. 2008, Article ID 493751 (2008)

    Article  Google Scholar 

  30. C. Park, Fuzzy stability of a functional equation associated with inner product spaces. Fuzzy Sets Syst. 160, 1632–1642 (2009)

    Article  MathSciNet  Google Scholar 

  31. Th.M. Rassias, On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)

    Article  MathSciNet  Google Scholar 

  32. Th.M. Rassias, Problem 16; 2. Report of the 27th International Symposium on Functional Equations. Aequations Math. 39, 292–293 (1990)

    Google Scholar 

  33. Th.M. Rassias, On the stability of the quadratic functional equation and its applications. Studia Univ. Babes-Bolyai. XLIII 89–124 (1998)

    Google Scholar 

  34. Th.M. Rassias, The problem of S.M. Ulam for approximately multiplicative mappings. J. Math. Anal. Appl. 246, 352–378 (2000)

    Article  MathSciNet  Google Scholar 

  35. Th.M. Rassias, On the stability of functional equations in Banach spaces. J. Math. Anal. Appl. 251, 264–284 (2000)

    Article  MathSciNet  Google Scholar 

  36. Th.M. Rassias, Functional Equations, Inequalities and Applications (Kluwer Academic Publishers Co., Dordrecht, 2003)

    Book  Google Scholar 

  37. Th.M. Rassias, P. Semrl, On the behaviour of mappings which do not satisfy Hyers-Ulam stability. Proc. Am. Math. Soc. 114 989–993 (1992)

    Article  Google Scholar 

  38. Th.M. Rassias, P. Semrl, On the Hyers-Ulam stability of linear mappings. J. Math. Anal. Appl. 173, 325–338 (1993)

    Article  MathSciNet  Google Scholar 

  39. K. Ravi, B.V.S. Kumar, Ulam stability of generalized reciprocal functional equation in several variables. Int. J. Appl. Math. Stat. 19(D10), 1–19 (2010)

    MathSciNet  Google Scholar 

  40. R. Saadati, C. Park, Non-Archimedean \(\mathcal {L}\)-fuzzy normed spaces and stability of functional equations. Comput. Math. Appl. 60(8), 2488–2496 (2010)

    Google Scholar 

  41. R. Saadati, M. Vaezpour, Y.J. Cho, A note to paper “On the stability of cubic mappings and quartic mappings in random normed spaces”. J. Inequal. Appl. 2009, Article ID 214530. https://doi.org/10.1155/2009/214530

  42. R. Saadati, M.M. Zohdi, S.M. Vaezpour, Nonlinear L-random stability of an ACQ functional equation. J. Inequal. Appl. 2011, Article ID 194394, 23 pp. https://doi.org/10.1155/2011/194394

  43. B. Schewizer, A. Sklar, Probabilistic Metric Spaces. North-Holland Series in Probability and Applied Mathematics (North-Holland, New York, 1983)

    Google Scholar 

  44. F. Skof, Local properties and approximation of operators. Rend. Sem. Mat. Fis. Milano 53, 113–129 (1983)

    Article  MathSciNet  Google Scholar 

  45. S.M. Ulam, Problems in Modern Mathematics. Science Editions (Wiley, New York, 1964)

    MATH  Google Scholar 

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Correspondence to Hassan Azadi Kenary .

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Kenary, H.A., Rassias, T.M. (2018). NAN-RN Approximately Generalized Additive Functional Equations. In: Rassias, T. (eds) Applications of Nonlinear Analysis . Springer Optimization and Its Applications, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-319-89815-5_16

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