On the probabilistic stability of the monomial functional equation

Volume 6, Issue 1, pp 51--59 http://dx.doi.org/10.22436/jnsa.006.01.08

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1706 Downloads
• 3163 Views

Authors

Claudia Zaharia - Department of Mathematics, West University of Timisoara, Bd. V. Parvan 4, 300223, Timisoara, Romania.

Abstract

Using the fixed point method, we establish a generalized Ulam - Hyers stability result for the monomial functional equation in the setting of complete random \(p\)-normed spaces. As a particular case, we obtain a new stability theorem for monomial functional equations in \(\beta\)-normed spaces.

Share and Cite

Keywords

• Random p-normed space
• Hyers - Ulam - Rassias stability
• monomial functional equation.

MSC

•  39B82
•  54E40

References

• [1] M. Albert and J. A. Baker, Functions with bounded n-th differences, Ann. Polonici Math., 43 (1983), 93-103.


• [2] T. Aoki , On the stability of the linear transformation in Banach spaces , J. Math. Soc. Japan, 2 (1950), 64-66.


• [3] L. Cădariu, V. Radu, Remarks on the stability of monomial functional equations, Fixed Point Theory , 8 (2007), 201-218.


• [4] L. Cădariu, V. Radu, Fixed points and generalized stability for functional equations in abstract spaces, J. Math. Inequal., 3 (2009), 463-473.


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


• [6] A. Gilányi , A characterization of monomial functions , Aequationes Math. , 54 (1997), 289-307.


• [7] A. Gilányi, Hyers - Ulam stability of monomial functional equations on a general domain, Proc. Natl. Acad. Sci. USA , 96 (1999), 10588-10590.


• [8] A. Gilányi , On the stability of monomial functional equations, Publ. Math. Debrecen, 56 (2000), 201-212.


• [9] I. Goleţ , Random p-normed spaces and applications to random functions, Istambul Univ. Fen Fak., Mat. Fiz. Astro. Derg., 1 (2004-2005), 31-42.


• [10] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA, 27 (1941), 222-224.


• [11] C. F. K. Jung , On generalized complete metric spaces, Bull. Amer. Math. Soc. , 75 (1969), 113-116.


• [12] D. Miheţ , The fixed point method for fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems, 160 (2009), 1663-1667.


• [13] D. Miheţ, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl., 343 (2008), 567-572.


• [14] D. Miheţ, The probabilistic stability for a functional equation in a single variable, Acta Mathematica Hungarica, 123 (2009), 249-256.


• [15] D. Miheţ, R. Saadati, S. M. Vaezpour, The stability of an additive functional equation in Menger probabilistic \(\varphi\)-normed spaces, Math. Slovaca , 61 (2011), 817-826.


• [16] A. K. Mirmostafaee, M. S. Moslehian, Fuzzy versions of the Hyers - Ulam - Rassias theorem, Fuzzy Sets and Systems, 159 (2008), 720-729.


• [17] A. K. Mirmostafaee, M. Mirzavaziri, M. S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems, 159 (2008), 730-738.


• [18] A. K. Mirmostafaee, Stability of monomial functional equation in quasi normed spaces, Bull. Korean Math. Soc. , 47 (2010), 777-785.


• [19] A. K. Mirmostafaee , Non-Archimedean stability of the monomial functional equations, Tamsui Oxford Journal of Mathematical Sciences, 26 (2010), 221-235.


• [20] V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory, 4 (2003), 91-96.


• [21] Th. M. Rassias , On the stability of linear mappings in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.


• [22] S. M. Ulam, Problems in Modern Mathematics, Chapter VI , Science Editions, Wiley, New York (1964)


• [23] C. Zaharia, D. Miheţ , On the probabilistic stability of some functional equations, Carpathian Journal of Mathematics, (accepted)