TY - JOUR AU - Zaharia, Claudia PY - 2013 TI - On the probabilistic stability of the monomial functional equation JO - Journal of Nonlinear Sciences and Applications SP - 51--59 VL - 6 IS - 1 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.006.01.08 DO - 10.22436/jnsa.006.01.08 ID - Zaharia2013 ER - TY - JOUR TI - Functions with bounded n-th differences AU - M. Albert and J. A. Baker JO - Ann. Polonici Math. PY - 1983 DA - 1983// VL - 43 ID - Baker1983 ER - TY - JOUR TI - On the stability of the linear transformation in Banach spaces AU - T. Aoki JO - J. Math. Soc. Japan PY - 1950 DA - 1950// VL - 2 ID - Aoki 1950 ER - TY - JOUR TI - Remarks on the stability of monomial functional equations AU - L. Cădariu AU - V. Radu JO - Fixed Point Theory PY - 2007 DA - 2007// VL - 8 ID - Cădariu2007 ER - TY - JOUR TI - Fixed points and generalized stability for functional equations in abstract spaces AU - L. Cădariu AU - V. Radu JO - J. Math. Inequal. PY - 2009 DA - 2009// VL - 3 ID - Cădariu2009 ER - TY - JOUR TI - A generalization of the Hyers - Ulam - Rassias stability of approximately additive mappings AU - P. Găvruţa JO - J. Math. Anal. Appl. PY - 1994 DA - 1994// VL - 184 ID - Găvruţa 1994 ER - TY - JOUR TI - A characterization of monomial functions AU - A. Gilányi JO - Aequationes Math. PY - 1997 DA - 1997// VL - 54 ID - Gilányi 1997 ER - TY - JOUR TI - Hyers - Ulam stability of monomial functional equations on a general domain AU - A. Gilányi JO - Proc. Natl. Acad. Sci. USA PY - 1999 DA - 1999// VL - 96 ID - Gilányi1999 ER - TY - JOUR TI - On the stability of monomial functional equations AU - A. Gilányi JO - Publ. Math. Debrecen PY - 2000 DA - 2000// VL - 56 ID - Gilányi 2000 ER - TY - JOUR TI - Random p-normed spaces and applications to random functions AU - I. Goleţ JO - Istambul Univ. Fen Fak., Mat. Fiz. Astro. Derg. PY - 2004-2005 DA - 2004-2005// VL - 1 ID - Goleţ 2004-2005 ER - TY - JOUR TI - On the stability of the linear functional equation AU - D. H. Hyers JO - Proc. Natl. Acad. Sci. USA PY - 1941 DA - 1941// VL - 27 ID - Hyers1941 ER - TY - JOUR TI - On generalized complete metric spaces AU - C. F. K. Jung JO - Bull. Amer. Math. Soc. PY - 1969 DA - 1969// VL - 75 ID - Jung 1969 ER - TY - JOUR TI - The fixed point method for fuzzy stability of the Jensen functional equation AU - D. Miheţ JO - Fuzzy Sets and Systems PY - 2009 DA - 2009// VL - 160 ID - Miheţ 2009 ER - TY - JOUR TI - On the stability of the additive Cauchy functional equation in random normed spaces AU - D. Miheţ AU - V. Radu JO - J. Math. Anal. Appl. PY - 2008 DA - 2008// VL - 343 ID - Miheţ2008 ER - TY - JOUR TI - The probabilistic stability for a functional equation in a single variable AU - D. Miheţ JO - Acta Mathematica Hungarica PY - 2009 DA - 2009// VL - 123 ID - Miheţ2009 ER - TY - JOUR TI - The stability of an additive functional equation in Menger probabilistic \(\varphi\)-normed spaces AU - D. Miheţ AU - R. Saadati AU - S. M. Vaezpour JO - Math. Slovaca PY - 2011 DA - 2011// VL - 61 ID - Miheţ2011 ER - TY - JOUR TI - Fuzzy versions of the Hyers - Ulam - Rassias theorem AU - A. K. Mirmostafaee AU - M. S. Moslehian JO - Fuzzy Sets and Systems PY - 2008 DA - 2008// VL - 159 ID - Mirmostafaee2008 ER - TY - JOUR TI - Fuzzy stability of the Jensen functional equation AU - A. K. Mirmostafaee AU - M. Mirzavaziri AU - M. S. Moslehian JO - Fuzzy Sets and Systems PY - 2008 DA - 2008// VL - 159 ID - Mirmostafaee2008 ER - TY - JOUR TI - Stability of monomial functional equation in quasi normed spaces AU - A. K. Mirmostafaee JO - Bull. Korean Math. Soc. PY - 2010 DA - 2010// VL - 47 ID - Mirmostafaee2010 ER - TY - JOUR TI - Non-Archimedean stability of the monomial functional equations AU - A. K. Mirmostafaee JO - Tamsui Oxford Journal of Mathematical Sciences PY - 2010 DA - 2010// VL - 26 ID - Mirmostafaee 2010 ER - TY - JOUR TI - The fixed point alternative and the stability of functional equations AU - V. Radu JO - Fixed Point Theory PY - 2003 DA - 2003// VL - 4 ID - Radu2003 ER - TY - JOUR TI - On the stability of linear mappings in Banach spaces AU - Th. M. Rassias JO - Proc. Amer. Math. Soc. PY - 1978 DA - 1978// VL - 72 ID - Rassias 1978 ER - TY - BOOK TI - Problems in Modern Mathematics, Chapter VI AU - S. M. Ulam PB - Science Editions, Wiley PY - 1964 DA - 1964// CY - New York ID - Ulam1964 ER - TY - BOOK TI - On the probabilistic stability of some functional equations AU - C. Zaharia AU - D. Miheţ PB - Carpathian Journal of Mathematics PY - accepted DA - accepted// CY - ID - Zahariaaccepted ER -