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Stability of Functional Equations in Random Normed Spaces pp 11–45Cite as

Generalized Spaces

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 86))

Abstract

In this chapter, we present some generalized spaces and their properties for the main results in this chapter.

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References

  1. C. Alsina, B. Schweizer, A. Sklar, On the definition of a probabilistic normed space. Aequ. Math. 46, 91–98 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. C. Alsina, B. Schweizer, A. Sklar, Continuity properties of probabilistic norms. J. Math. Anal. Appl. 208, 446–452 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. T.M. Apostol, Mathematical Analysis, 2nd edn. (Addison-Wesley, Reading, 1975)

    Google Scholar 

  4. G. Deschrijver, E.E. Kerre, On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst. 23, 227–235 (2003)

    Article  MathSciNet  Google Scholar 

  5. I. Goleţ, Some remarks on functions with values in probabilistic normed spaces. Math. Slovaca 57, 259–270 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. K. Hensel, Über eine neue Begrundung der Theorie der algebraischen Zahlen. Jahresber. Dtsch. Math.-Ver. 6, 83–88 (1897)

    Google Scholar 

  7. B. Lafuerza-Guillén, A. Rodríguez-Lallena, C. Sempi, A study of boundedness in probabilistic normed spaces. J. Math. Anal. Appl. 232, 183–196 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Miheţ, R. Saadati, S.M. Vaezpour, The stability of the quartic functional equation in random normed spaces. Acta Appl. Math. 110, 797–803 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Miheţ, R. Saadati, S.M. Vaezpour, The stability of an additive functional equation in Menger probabilistic φ-normed spaces. Math. Slovaca 61, 817–826 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. A.K. Mirmostafaee, M.S. Moslehian, Fuzzy stability of additive mappings in non-Archimedean fuzzy normed spaces. Fuzzy Sets Syst. 160, 1643–1652 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. D.H. Mushtari, On the linearity of isometric mappings on random normed spaces. Kazan Gos. Univ. Uchen. Zap. 128, 86–90 (1968)

    MATH  Google Scholar 

  12. V. Radu, Some remarks on quasi-normed and random normed structures, in Seminar on Probability Theory and Applications (STPA), vol. 159 (West Univ. of Timişoara, Timişoara, 2003)

    Google Scholar 

  13. B. Schweizer, A. Sklar, Probabilistic Metric Spaces (Elsevier, North Holland, 1983)

    MATH  Google Scholar 

  14. A.N. Šerstnev, On the motion of a random normed space. Dokl. Akad. Nauk SSSR 149, 280–283 (1963) (English translation in Sov. Math. Dokl. 4, 388–390 (1963))

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Education, Department of Mathematics Education, Gyeongsang National University, Chinju, Republic of South Korea

    Yeol Je Cho

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  3. Department of Mathematics, Iran University of Science and Technology, Behshahr, Iran

    Reza Saadati

Authors
  1. Yeol Je Cho
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  2. Themistocles M. Rassias
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  3. Reza Saadati
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Cho, Y.J., Rassias, T.M., Saadati, R. (2013). Generalized Spaces. In: Stability of Functional Equations in Random Normed Spaces. Springer Optimization and Its Applications, vol 86. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8477-6_2

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