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The probabilistic stability for a functional equation in a single variable

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Abstract

We discuss the probabilistic stability of the equation µ ∘ f ∘ η = f, by using the fixed point method.

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References

  1. T. Aoki, On the stability of the linear transformation in Banach spaces, J. M. Soc. Japan, 2 (1950), 64–66.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. A. Baker, The stability of certain functional equations, Proc. Amer. Math. Soc., 112 (1991), 729–732.

    Article  MATH  MathSciNet  Google Scholar 

  3. L. Cădariu and V. Radu, Fixed point method for the generalized stability of functional equations in single variable, Fixed Point Theory and Applications, vol. 2008, Article ID 749392 (2008), 15 pages.

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

    MATH  Google Scholar 

  5. G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math., 50 (1995), 143–190.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Gianyi, Z. Kaiser and Z. Páles, Estimates to the stability of functional equations, Aequationes Math., 73 (2007), 125–143.

    Article  MathSciNet  Google Scholar 

  8. O. Hadžić, A generalization of the contraction principle in PM-spaces, Zb. Rad. Prirod. Mat. Fak. Univ. u Novom Sadu, 10 (1980), 13–21.

    MATH  Google Scholar 

  9. O. Hadžić and E. Pap, Fixed Point Theory in PM Spaces, Kluwer Academic Publ. (2001).

  10. O. Hadzic, E. Pap and V. Radu, Generalized contraction mapping principles in probabilistic metric spaces, Acta Math. Hungar., 101 (2003), 131–148.

    Article  MATH  MathSciNet  Google Scholar 

  11. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222–224.

    Article  MathSciNet  Google Scholar 

  12. D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equations in Several Variables (Basel, 1998).

  13. I. Istrăţescu, On generalized Menger spaces, Boll. UMI (5) 13-A (1976), 95–100.

    Google Scholar 

  14. C. F. K. Jung, On generalized complete metric spaces, Bull. Amer. Math. Soc., 75 (1969), 113–116.

    Article  MATH  MathSciNet  Google Scholar 

  15. Z. Kominek, On a local stability of the Jensen functional equation, Demonstratio Math., 22 (1989), 499–507.

    MATH  MathSciNet  Google Scholar 

  16. W. A. J. Luxemburg, On the convergence of successive approximations in the theory of ordinary differential equations, II, Nederl. Akad. Wetensch. Proc. Ser. A 61 = Indag. Math., 20 (1958), 540–546.

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  19. M. Mirmostafaee, M. Mirzavaziri and M. S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems, 159 (2008), 730–738.

    Article  MathSciNet  MATH  Google Scholar 

  20. A. K. Mirmostafee and M. S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems, 159 (2008), 720–729.

    Article  MathSciNet  Google Scholar 

  21. V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory, Cluj-Napoca, IV(1) (2003), 91–96.

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  23. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland (1983).

  24. V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on PM-Spaces, Math. Syst. Theory, 6 (1972), 97–100.

    Article  MATH  MathSciNet  Google Scholar 

  25. N. X. Tan, Generalized probabilistic metric spaces and fixed point theorems, Math. Nachr., 129 (1986), 205–218.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Department of Mathematics, West University of Timişoara, Vasile Pârvan 4, 300223, Timişoara, Romania

    D. Miheƫ

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  1. D. Miheƫ
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Miheƫ, D. The probabilistic stability for a functional equation in a single variable. Acta Math Hung 123, 249–256 (2009). https://doi.org/10.1007/s10474-008-8101-y

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  • DOI: https://doi.org/10.1007/s10474-008-8101-y

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