TY - JOUR AU - Park, Yuanfeng AU - Lu, Yinhua AU - Cui, Gang AU - Jin, Choonkil PY - 2017 TI - Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces JO - Journal of Nonlinear Sciences and Applications SP - 104--110 VL - 10 IS - 1 AB - In this paper, we solve the quadratic \(\rho\)-functional inequalities \[\|f(x+y)+f(x-y)-2f(x)-2f(y)\|\leq\|\rho(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y))\|,\] where \(\rho\) is a fixed complex number with \(|\rho|<1\), and\[\|4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)\|\leq\|\rho(f(x+y)+f(x-y)-2f(x)-2f(y))\|,\] where \(\rho\) is a fixed complex number with \(|\rho|<1\). Using the direct method, we prove the Hyers-Ulam stability of the quadratic \(\rho\)-functional inequalities (1) and (2) in \(\beta\)- homogeneous complex Banach spaces. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.01.10 DO - 10.22436/jnsa.010.01.10 ID - Park2017 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 functional equations AU - P. W. Cholewa JO - Aequationes Math. PY - 1984 DA - 1984// VL - 27 ID - Cholewa1984 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 - JOUR TI - Additive \(\rho\)-functional inequalities and equations AU - C.-K. Park JO - J. Math. Inequal. PY - 2015 DA - 2015// VL - 9 ID - Park2015 ER - TY - JOUR TI - Additive \(\rho\)-functional inequalities in non-Archimedean normed spaces AU - C.-K. Park JO - J. Math. Inequal. PY - 2015 DA - 2015// VL - 9 ID - Park 2015 ER - TY - JOUR TI - Approximate \(\eta\)-Jordan \(*\)-homomorphisms in \(C^*\)-algebras AU - C.-K. Park AU - K. Ghasemi AU - S. G. Ghaleh AU - S. Y. Jang JO - J. Comput. Anal. Appl. PY - 2013 DA - 2013// VL - 15 ID - Park2013 ER - TY - JOUR TI - Fixed points and fuzzy stability of an additive-quadratic functional equation AU - C.-K. Park AU - A. Najati AU - S. Y. Jang JO - J. Comput. Anal. Appl. PY - 2013 DA - 2013// VL - 15 ID - Park2013 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 - BOOK TI - Metric linear spaces, Monografie Matematyczne AU - S. Rolewicz PB - Tom, [Mathematical Monographs] PWN-Polish Scientific Publishers PY - 1972 DA - 1972// CY - Warsaw ID - Rolewicz 1972 ER - TY - JOUR TI - Nearly ternary cubic homomorphism in ternary Fréchet algebras AU - S. Shagholi AU - M. E. Gordji AU - M. Bavand Savadkouhi JO - J. Comput. Anal. Appl. PY - 2011 DA - 2011// VL - 13 ID - Shagholi2011 ER - TY - JOUR TI - Stability of ternary quadratic derivation on ternary Banach algebras AU - S. Shagholi AU - M. E. Gordji AU - M. Bavand Savadkouhi JO - J. Comput. Anal. Appl. PY - 2011 DA - 2011// VL - 13 ID - Shagholi2011 ER - TY - JOUR TI - On the superstability of ternary Jordan \(C^*\)-homomorphisms AU - D. Y. Shin AU - C.-K. Park AU - S. Farhadabadi JO - J. Comput. Anal. Appl. PY - 2014 DA - 2014// VL - 16 ID - Shin2014 ER - TY - JOUR TI - Stability and superstability of \(J^*\)-homomorphisms and \(J^*\)-derivations for a generalized Cauchy-Jensen equation AU - D. Y. Shin AU - C.-K. Park AU - S. Farhadabadi JO - J. Comput. Anal. Appl. PY - 2014 DA - 2014// VL - 17 ID - Shin2014 ER - TY - JOUR TI - Proprietà locali e approssimazione di operatori AU - F. Skof JO - Rend. Sem. Mat. Fis. Milano PY - 1983 DA - 1983// VL - 53 ID - Skof1983 ER - TY - BOOK TI - A collection of mathematical problems AU - S. M. Ulam PB - Interscience Tracts in Pure and Applied Mathematics, Interscience Publishers PY - 1960 DA - 1960// CY - New York-London ID - Ulam1960 ER -