TY - JOUR AU - Bae, Jae-Hyeong AU - Chang, Ick-Soon PY - 2018 TI - Some additive mappings on Banach \({\ast}\)-algebras with derivations JO - Journal of Nonlinear Sciences and Applications SP - 335--341 VL - 11 IS - 3 AB - We take into account some additive mappings in Banach \(\ast\)-algebras with derivations. We will first study the conditions for additive mappings with derivations on Banach \(\ast\)-algebras. Then we prove some theorems involving linear mappings on Banach $\ast$-algebras with derivations. So derivations on \(C^{\ast}\)-algebra are characterized. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.011.03.02 DO - 10.22436/jnsa.011.03.02 ID - Bae2018 ER - TY - JOUR TI - Approximation of the multiplicatives on random multi-normed space AU - R. P. Agarwal AU - R. Saadati AU - A. Salamati JO - J. Inequal. Appl. PY - 2017 DA - 2017 // VL - 2017 ID - Agarwal2017 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 - JOUR TI - Generalized stability of Euler-Lagrange quadratic functional equation in random normed spaces under arbitrary t-norms AU - Z. Baderi AU - R. Saadati JO - Thai J. Math. PY - 2016 DA - 2016// VL - 14 ID - Baderi2016 ER - TY - JOUR TI - On approximate ring homomorphisms AU - R. Badora JO - J. Math. Anal. Appl. PY - 2002 DA - 2002// VL - 276 ID - Badora 2002 ER - TY - JOUR TI - On approximate derivations AU - R. Badora JO - Math. Inequal. Appl. PY - 2006 DA - 2006// VL - 9 ID - Badora 2006 ER - TY - BOOK TI - Complete normed algebras AU - F. F. Bonsall AU - J. Duncan PB - Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer- Verlag PY - 1973 DA - 1973// CY - New York-Heidelberg ID - Bonsall1973 ER - TY - JOUR TI - Approximately isometric and multiplicative transformations on continuous function rings AU - D. G. Bourgin JO - Duke Math. J. PY - 1949 DA - 1949// VL - 16 ID - Bourgin1949 ER - TY - JOUR TI - On some additive mappings in rings with involution AU - M. Brešar AU - J. Vukman JO - Aequationes Math. PY - 1989 DA - 1989// VL - 38 ID - Brešar1989 ER - TY - JOUR TI - On left derivations and related mappings AU - M. Brešar AU - J. Vukman JO - Proc. Amer. Math. Soc. PY - 1990 DA - 1990// VL - 110 ID - Brešar1990 ER - TY - BOOK TI - Stability of functional equations in Banach algebras AU - Y. J. Cho AU - C.-K. Park AU - T. M. Rassias AU - R. Saadati PB - Springer PY - 2015 DA - 2015// CY - Cham ID - Cho2015 ER - TY - JOUR TI - On generalized derivations of semiprime rings with involution AU - M. N. Daif AU - M. S. Tammam El-Sayiad JO - Int. J. Algebra PY - 2007 DA - 2007// VL - 1 ID - Daif2007 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 - Nearly involutions on Banach algebras AU - M. E. Gordji JO - A fixed point approach, Fixed Point Theory PY - 2013 DA - 2013// VL - 14 ID - Gordji 2013 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 - 1911 DA - 1911// VL - 27 ID - Hyers1911 ER - TY - JOUR TI - Continuity of derivations and a problem of Kaplansky AU - B. E. Johnson AU - A. M. Sinclair JO - Amer. J. Math. PY - 1968 DA - 1968// VL - 90 ID - Johnson1968 ER - TY - BOOK TI - Functional equations and inequalities with applications AU - P. Kannappan PB - Springer Monographs in Mathematics, Springer PY - 2009 DA - 2009// CY - New York ID - Kannappan2009 ER - TY - BOOK TI - Analytic number theory, approximation theory, and special functions AU - G. V. Milovanović(ed.) AU - T. M. Rassias (ed.) PB - In honor of Hari M. Srivastava, Springer PY - 2014 DA - 2014// CY - New York ID - Milovanović(ed.)2014 ER - TY - JOUR TI - Functional inequalities in fuzzy normed spaces AU - C.-K. Park AU - G. A. Anastassiou AU - R. Saadati AU - S.-S. Yun JO - J. Comput. Anal. Appl. PY - 2017 DA - 2017// VL - 22 ID - Park2017 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 - The functional equation of multiplicative derivation is superstable on standard operator algebras AU - P. Šemrl JO - Integral Equations Operator Theory PY - 1994 DA - 1994// VL - 18 ID - Šemrl1994 ER - TY - JOUR TI - Derivations on commutative normed algebras AU - I. M. Singer AU - J. Wermer JO - Math. Ann. PY - 1955 DA - 1955// VL - 129 ID - Singer1955 ER - TY - JOUR TI - The image of a derivation is contained in the radical AU - M. P. Thomas JO - Ann. of Math. PY - 1988 DA - 1988// VL - 128 ID - Thomas1988 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 - Ulam 1960 ER -