%0 Journal Article %T On the stability of an affine functional equation %A Cădariu, Liviu %A Găvruţa, Laura %A Găvruţa, Paşc %J Journal of Nonlinear Sciences and Applications %D 2013 %V 6 %N 2 %@ ISSN 2008-1901 %F Cădariu2013 %X In this paper, we obtain the general solution and we prove the generalized Hyers-Ulam stability for an affine functional equation. %9 journal article %R 10.22436/jnsa.006.02.01 %U http://dx.doi.org/10.22436/jnsa.006.02.01 %P 60--67 %0 Journal Article %T On the stability of the linear transformation in Banach spaces %A T. Aoki %J J. Math. Soc. Japan %D 1950 %V 2 %F Aoki 1950 %0 Journal Article %T The stability of certain functional equations %A J. A. Baker %J Proc. AMS %D 1991 %V 112(3) %F Baker 1991 %0 Journal Article %T A fixed point approach to the stability of functional equations in non-Archimedean metric spaces %A J. Brzdęk %A K. Ciepliński %J Nonlinear Analysis - TMA %D 2011 %V 74 %F Brzdęk2011 %0 Journal Article %T Weighted space method for the stability of some nonlinear equations %A L. Cădariu %A L. Găvruţa %A P. Găvruţa %J Appl. Anal. Discrete Math. %D 2012 %V 6 %F Cădariu2012 %0 Journal Article %T Fixed points and generalized Hyers-Ulam stability %A L. Cădariu %A L. Găvruţa %A P. Găvruţa %J Abstr. Appl. Anal. Article ID 712743 %D 2012 %V 2012 %F Cădariu2012 %0 Journal Article %T Fixed points and the stability of Jensen's functional equation %A L. Cădariu %A V. Radu %J J. Inequal. Pure and Appl. Math., Art. 4 %D 2003 %V 4(1) %F Cădariu2003 %0 Journal Article %T On the stability of the Cauchy functional equation: a fixed points approach, Iteration theory (ECIT '02) %A L. Cădariu %A V. Radu %J (J. Sousa Ramos, D. Gronau, C. Mira, L. Reich, A. N. Sharkovsky - Eds.)Grazer Math. Ber. %D 2004 %V 346 %F Cădariu2004 %0 Journal Article %T Fixed point methods for the generalized stability of functional equations in a single variable %A L. Cădariu L. %A V. Radu %J Fixed Point Theory and Applications, Article ID 749392 %D 2008 %V 2008 %F L.2008 %0 Book %T A general fixed point method for the stability of Cauchy functional equation %A L. Cădariu L. %A V. Radu %D 2011 %I in Functional Equations in Mathematical Analysis, Th. M. Rassias, J. Brzdek (Eds.), Series Springer Optimization and Its Applications 52 %C %F L.2011 %0 Journal Article %T A general fixed point method for the stability of the monomial functional equation %A L. Cădariu L. %A V. Radu %J Carpathian J. Math. %D 2012 %V 28 %F L.2012 %0 Book %T On the Hyers-Ulam Stability of Quadratic Functional Equations %A I.-S. Chang %A H.-M. Kim %D 2002 %I 3(3) %C %F Chang2002 %0 Book %T Functional Equations and Inequalities in Several Variables %A S. Czerwik %D 2002 %I World Scientific Publishing Company, New Jersey, London %C Singapore Hong Kong %F Czerwik2002 %0 Journal Article %T A fixed point theorem of the alternative for contractions on a generalized complete metric space %A J. B. Diaz %A B. Margolis %J Bull. Amer. Math. Soc. %D 1968 %V 74 %F Diaz1968 %0 Journal Article %T An existence and stability theorem for a class of functional equations %A G. L. Forti %J Stochastica %D 1980 %V 4 %F Forti1980 %0 Journal Article %T Hyers-Ulam stability of functional equations in several variables %A G. L. Forti %J Aeq. Math. %D 1995 %V 50 %F Forti 1995 %0 Journal Article %T Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations %A G. L. Forti %J J. Math. Anal. Appl. %D 2004 %V 295(1) %F Forti2004 %0 Journal Article %T On stability of additive mappings %A Z. Gajda %J Internat. J. Math. Math. Sci. %D 1991 %V 14 %F Gajda1991 %0 Journal Article %T Matkowski contractions and Hyers-Ulam stability %A L. Găvruţa %J Bul. Şt. Univ. ''Politehnica'' Timişoara, Seria Mat.-Fiz. %D 2008 %V 53(67) %F Găvruţa2008 %0 Journal Article %T A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings %A P. Găvruţa %J J. Math. Anal. Appl. %D 1994 %V 184 %F Găvruţa1994 %0 Journal Article %T On a problem of G. Isac and Th. M. Rassias concerning the stability of mappings %A P. Găvruţa %J J. Math. Anal. Appl. %D 2001 %V 261 %F Găvruţa2001 %0 Journal Article %T A new method for the generalized Hyers-Ulam-Rassias stability %A P. Găvruţa %A L. Găvruţa %J Int. J. Nonlinear Anal. Appl. %D 2010 %V 1 %F Găvruţa2010 %0 Journal Article %T On the stability of the linear functional equation %A D. H. Hyers %J Prod. Natl. Acad. Sci. USA %D 1941 %V 27 %F Hyers1941 %0 Book %T Stability of Functional Equations in Several Variables %A D. H. Hyers %A G. Isac G. %A Th. M. Rassias %D 1998 %I Birkhauser %C Basel %F Hyers1998 %0 Book %T Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis %A S.-M. Jung %D 2011 %I Series Springer Optimization and Its Applications %C Springer %F Jung2011 %0 Journal Article %T The Hyers-Ulam stability for two functional equations in a single variable %A D. Miheţ %J Banach J. Math. Anal. Appl. %D 2008 %V 2 %F Miheţ 2008 %0 Journal Article %T The fixed point alternative and the stability of functional equations %A V. Radu %J Fixed Point Theory %D 2003 %V 4 %F Radu2003 %0 Journal Article %T On the stability of the linear mapping in Banach spaces %A Th. M. Rassias %J Proc. Amer. Math. Soc. %D 1978 %V 72 %F Rassias1978 %0 Journal Article %T On the stability of functional equations and a problem of Ulam %A Th. M. Rassias %J Acta Appl. Math. %D 2000 %V 62 %F Rassias2000 %0 Book %T Problems in Modern Mathematics, Chapter VI %A S. M. Ulam %D 1964 %I Science Editions, Wiley %C New York %F Ulam1964