Stability of Mixed Type Cubic and Quartic Functional Equations in Random Normed Spaces

We obtain the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary -norms .

[1]  Zbigniew Gajda,et al.  On stability of additive mappings , 1991 .

[2]  P. K. Sahoo,et al.  ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION , 2003 .

[3]  Reza Saadati,et al.  Erratum to: A Note to Paper "On the Stability of Cubic Mappings and Quartic Mappings in Random Normed Spaces" , 2009 .

[4]  Endre Pap,et al.  Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces , 2002, Kybernetika.

[5]  K. Jun,et al.  The generalized Hyers–Ulam–Rassias stability of a cubic functional equation☆ , 2002 .

[6]  Chun-Gil Park On the Stability of the Orthogonally Quartic Functional Equation , 2005 .

[7]  D. G. Bourgin Classes of transformations and bordering transformations , 1951 .

[8]  Won-Gil Park,et al.  On a bi-quadratic functional equation and its stability , 2005 .

[9]  Dorel Mihet,et al.  The fixed point method for fuzzy stability of the Jensen functional equation , 2009, Fuzzy Sets Syst..

[10]  Endre Pap,et al.  Fixed Point Theory in Probabilistic Metric Spaces , 2001 .

[11]  P. Gǎvruţa,et al.  A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings , 1994 .

[12]  D. Miheƫ,et al.  The probabilistic stability for a functional equation in a single variable , 2009 .

[13]  S. Ulam Problems in modern mathematics , 1964 .

[14]  Themistocles M. Rassias,et al.  On the Stability of Functional Equations in Banach Spaces , 2000 .

[15]  Dorel Mihet,et al.  On the stability of the additive Cauchy functional equation in random normed spaces , 2011, Appl. Math. Lett..

[16]  George Isac,et al.  Stability of Functional Equations in Several Variables , 1998 .

[17]  S. M. Vaezpour,et al.  The Stability of the Quartic Functional Equation in Random Normed Spaces , 2010 .

[18]  M. Birkner,et al.  Blow-up of semilinear PDE's at the critical dimension. A probabilistic approach , 2002 .

[19]  Tosio Aoki,et al.  On the Stability of the linear Transformation in Banach Spaces. , 1950 .

[20]  Reza Saadati,et al.  On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces , 2008 .

[21]  Sang Han Lee,et al.  Quartic functional equations , 2005 .

[22]  George Isac,et al.  On the Hyers-Ulam Stability of ψ-Additive Mappings , 1993 .

[23]  A. Ebadian,et al.  Stability of a Functional Equation Deriving from Cubic and Quartic Functions , 2008, 0812.5020.

[24]  Viorel Radu,et al.  On the stability of the additive Cauchy functional equation in random normed spaces , 2008, Appl. Math. Lett..

[25]  D. H. Hyers On the Stability of the Linear Functional Equation. , 1941, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Themistocles M. Rassias,et al.  On the Stability of Functional Equations and a Problem of Ulam , 2000 .

[27]  T. Rassias On the stability of the linear mapping in Banach spaces , 1978 .

[28]  A. Najati On the stability of a quartic functional equation , 2008 .

[29]  Berthold Schweizer,et al.  Probabilistic Metric Spaces , 2011 .

[30]  M. Gordji,et al.  Solution and stability of generalized mixed type cubic , quadratic and additive functional equation in quasi-Banach spaces , 2008, 0812.2931.