TY - JOUR AU - Lu, Gang AU - Liu, Qi AU - Jin, Yuanfeng AU - Xie, Jun PY - 2016 TI - 3-variable Jensen \(\rho\)-functional inequalities and equations JO - Journal of Nonlinear Sciences and Applications SP - 5995--6003 VL - 9 IS - 12 AB - In this paper, we introduce and investigate Jensen \(\rho\)-functional inequalities associated with the following Jensen functional equations \[f(x + y + z) + f(x + y - z) - 2f(x) - 2f(y) = 0,\\ f(x + y + z) - f(x - y - z) - 2f(y) - 2f(z) = 0.\] We prove the Hyers-Ulam-Rassias stability of the Jensen \(\rho\)-functional inequalities in complex Banach spaces and prove the Hyers-Ulam-Rassias stability of the Jensen \(\rho\)-functional equations associated with the \(\rho\)- functional inequalities in complex Banach spaces. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.009.12.07 DO - 10.22436/jnsa.009.12.07 ID - Lu2016 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 - Aoki1950 ER - TY - BOOK TI - Functional equations in several variables, With applications to mathematics, information theory and to the natural and social sciences, Encyclopedia of Mathematics and its Applications AU - J. Aczél AU - J. Dhombres PB - Cambridge University Press PY - 1989 DA - 1989// CY - Cambridge ID - Aczél1989 ER - TY - JOUR TI - Fixed points and the stability of Jensen's functional equation AU - L. Cădariu AU - V. Radu JO - JIPAM. J. Inequal. Pure Appl. Math. PY - 2003 DA - 2003// VL - 4 ID - Cădariu2003 ER - TY - JOUR TI - Nearly quartic mappings in \(\beta\)-homogeneous F-spaces AU - I. S. Chang AU - M. Eshaghi Gordji AU - H. Khodaei AU - H. M. Kim JO - Results Math. PY - 2013 DA - 2013// VL - 63 ID - Chang2013 ER - TY - JOUR TI - Functional inequalities in non-Archimedean Banach spaces AU - Y. J. Cho AU - C. K. Park AU - R. Saadati JO - Appl. Math. Lett. PY - 2010 DA - 2010// VL - 23 ID - Cho2010 ER - TY - JOUR TI - Approximation of homomorphisms and derivations on Lie \(C^*\)-algebras via fixed point method AU - Y. J. Cho AU - R. Saadati AU - Y.-O. Yang JO - J. Inequal. Appl. PY - 2013 DA - 2013// VL - 2013 ID - Cho2013 ER - TY - JOUR TI - Remarks on the stability of functional equations AU - P. W. Cholewa JO - Aequationes Math. PY - 1984 DA - 1984// VL - 27 ID - Cholewa1984 ER - TY - JOUR TI - A fixed point theorem of the alternative, for contractions on a generalized complete metric space AU - J. B. Diaz AU - B. Margolis JO - Bull. Amer. Math. Soc. PY - 1968 DA - 1968// VL - 74 ID - Diaz1968 ER - TY - JOUR TI - Functional inequalities associated with Cauchy additive functional equation in non-Archimedean spaces AU - A. Ebadian AU - N. Ghobadipour AU - T. M. Rassias AU - M. Eshaghi Gordji JO - Discrete Dyn. Nat. Soc. PY - 2011 DA - 2011// VL - 2011 ID - Ebadian2011 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 - Găvruţa1994 ER - TY - JOUR TI - On the stability of the linear functional equation AU - D. H. Hyers JO - Proc. Nat. Acad. Sci. U. S. A. PY - 1941 DA - 1941// VL - 27 ID - Hyers1941 ER - TY - BOOK TI - Stability of functional equations in several variables, Progress in Nonlinear Differential Equations and their Applications AU - D. H. Hyers AU - G. Isac AU - T. M. Rassias PB - Birkhäuser Boston, Inc. PY - 1998 DA - 1998// CY - Boston ID - Hyers1998 ER - TY - JOUR TI - On the Hyers-Ulam stability of \(\psi\)-additive mappings AU - G. Isac AU - T. M. Rassias JO - J. Approx. Theory PY - 1993 DA - 1993// VL - 72 ID - Isac1993 ER - TY - BOOK TI - Theory of fractional dynamic systems AU - V. Lakshmikantham AU - S. Leela AU - J. Vasundhara Devi PB - Cambridge Scientific Publishers PY - 2009 DA - 2009// CY - ID - Lakshmikantham2009 ER - TY - JOUR TI - On the stability of an additive functional inequality for the fixed point alternative AU - S.-B. Lee AU - J.-H. Bae AU - W.-G. Park JO - J. Comput. Anal. Appl. PY - 2014 DA - 2014// VL - 17 ID - Lee2014 ER - TY - JOUR TI - Hyers-Ulam Stability of Additive Set-valued Functional Equations AU - G. Lu AU - C. K. Park JO - Appl. Math. Lett. PY - 2011 DA - 2011// VL - 24 ID - Lu2011 ER - TY - JOUR TI - Functional inequalities associated with Jordan-von Neumann-type additive functional equations AU - C. K. Park AU - Y. S. Cho AU - M.-H. Han JO - J. Inequal. Appl. PY - 2007 DA - 2007// VL - 2007 ID - Park2007 ER - TY - JOUR TI - On the stability of the linear mapping in Banach spaces AU - T. M. Rassias JO - Proc. Amer. Math. Soc. PY - 1978 DA - 1978// VL - 72 ID - Rassias1978 ER - TY - JOUR TI - On approximation of approximately linear mappings by linear mappings AU - J. M. Rassias JO - J. Funct. Anal. PY - 1982 DA - 1982// VL - 46 ID - Rassias1982 ER - TY - JOUR TI - On approximation of approximately linear mappings by linear mappings AU - J. M. Rassias JO - Bull. Sci. Math. PY - 1984 DA - 1984// VL - 108 ID - Rassias1984 ER - TY - JOUR TI - Solution of a problem of Ulam AU - J. M. Rassias JO - J. Approx. Theory PY - 1989 DA - 1989// VL - 57 ID - Rassias1989 ER - TY - JOUR TI - Complete solution of the multi-dimensional problem of Ulam AU - J. M. Rassias JO - Discuss. Math. PY - 1994 DA - 1994// VL - 14 ID - Rassias1994 ER - TY - BOOK TI - Functional equations and inequalities, Mathematics and its Applications AU - T. M. Rassias PB - Kluwer Academic Publishers PY - 2000 DA - 2000// CY - Dordrecht ID - Rassias2000 ER - TY - JOUR TI - On the stability of functional equations and a problem of Ulam AU - T. M. Rassias JO - Acta Math. Appl. PY - 2000 DA - 2000// VL - 62 ID - Rassias2000 ER - TY - JOUR TI - On the stability of functional equations in Banach spaces AU - T. M. Rassias JO - J. Math. Anal. Appl. PY - 2000 DA - 2000// VL - 251 ID - Rassias2000 ER - TY - JOUR TI - Refined Hyers-Ulam approximation of approximately Jensen type mappings AU - J. M. Rassias JO - Bull. Sci. Math. PY - 2007 DA - 2007// VL - 131 ID - Rassias2007 ER - TY - JOUR TI - On the Ulam stability of Jensen and Jensen type mappings on restricted domains AU - J. M. Rassias AU - M. J. Rassias JO - J. Math. Anal. Appl. PY - 2003 DA - 2003// VL - 281 ID - Rassias2003 ER - TY - BOOK TI - Problems in modern mathematics (Chapter VI) AU - S. M. Ulam PB - Wiley, PY - 1960 DA - 1960// CY - New York ID - Ulam1960 ER - TY - JOUR TI - A fixed point approach to the stability of a general mixed additive-cubic functional equation in quasi fuzzy normed spaces AU - T. Z. Xu AU - J. M. Rassias AU - W. X. Xu AU - JO - Int. J. Phys. Sci. PY - 2011 DA - 2011// VL - 6 ID - Xu2011 ER -