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NTIS 바로가기Journal of inequalities and applications, v.2012 no.1, 2012년, pp.83 -
Lee, Sung Jin , Park, Choonkil , Saadati, Reza
AbstractUsing the fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equationfor all x, y with x ⊥ y, where ⊥ is the orthogonality in the sense of Rätz.AMS Subject Classification: Primary, 39B55; 47H10; 39B52; 46H25....
C R (Dokl) Acad Sci URSS, n Ser AG Pinsker 20 411 1938 Pinsker AG: Sur une fonctionnelle dans l'espace de Hilbert. C R (Dokl) Acad Sci URSS, n Ser 1938, 20: 411-414.
Proc Am Math Soc K Sundaresan 34 187 1972 10.1090/S0002-9939-1972-0291835-X Sundaresan K: Orthogonality and nonlinear functionals on Banach spaces. Proc Am Math Soc 1972, 34: 187-190.
Pac J Math S Gudder 58 427 1975 10.2140/pjm.1975.58.427 Gudder S, Strawther D: Orthogonally additive and orthogonally increasing functions on vector spaces. Pac J Math 1975, 58: 427-436.
Aequationes Math J Rätz 28 35 1985 10.1007/BF02189390 Rätz J: On orthogonally additive mappings. Aequationes Math 1985, 28: 35-49.
Aequationes Math J Rätz 38 73 1989 10.1007/BF01839496 Rätz J, Szabó Gy: On orthogonally additive mappings IV . Aequationes Math 1989, 38: 73-85.
Main properties Extracta Math J Alonso 3 1 1988 Alonso J, Benítez C: Orthogonality in normed linear spaces: a survey I . Main properties Extracta Math 1988, 3: 1-15.
Relations between main orthogonalities Extracta Math J Alonso 4 121 1989 Alonso J, Benítez C: Orthogonality in normed linear spaces: a survey II . Relations between main orthogonalities Extracta Math 1989, 4: 121-131.
Duke Math J G Birkhoff 1 169 1935 10.1215/S0012-7094-35-00115-6 Birkhoff G: Orthogonality in linear metric spaces. Duke Math J 1935, 1: 169-172.
Ark Mat SO Carlsson 4 297 1962 10.1007/BF02591506 Carlsson SO: Orthogonality in normed linear spaces. Ark Mat 1962, 4: 297-318.
Math Nachr CR Diminnie 114 197 1983 10.1002/mana.19831140115 Diminnie CR: A new orthogonality relation for normed linear spaces. Math Nachr 1983, 114: 197-203.
Trans Am Math Soc RC James 61 265 1947 10.1090/S0002-9947-1947-0021241-4 James RC: Orthogonality and linear functionals in normed linear spaces. Trans Am Math Soc 1947, 61: 265-292.
SM Ulam 1960 Problems in Modern Mathematics Ulam SM: Problems in Modern Mathematics. Wiley, New York; 1960.
Proc Nat Acad Sci USA DH Hyers 27 222 1941 10.1073/pnas.27.4.222 Hyers DH: On the stability of the linear functional equation. Proc Nat Acad Sci USA 1941, 27: 222-224.
Proc Amer Math Soc ThM Rassias 72 297 1978 10.1090/S0002-9939-1978-0507327-1 Rassias ThM: On the stability of the linear mapping in Banach spaces. Proc Amer Math Soc 1978, 72: 297-300.
S Czerwik 2003 Hadronic Press, Palm Harbor, Florida Czerwik S: Stability of Functional Equations of Ulam-Hyers-Rassias Type. Hadronic Press, Palm Harbor, Florida 2003.
S Jung 2001 Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis Jung S: Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis. Hadronic Press, Palm Harbor, Florida; 2001.
Bull Polish Acad Sci Math R Ger 43 143 1995 Ger R, Sikorska J: Stability of the orthogonal additivity. Bull Polish Acad Sci Math 1995, 43: 143-151.
Rend Sem Mat Fis Milano F Skof 53 113 1983 10.1007/BF02924890 Skof F: Proprietà locali e approssimazione di operatori. Rend Sem Mat Fis Milano 1983, 53: 113-129.
Aequationes Math PW Cholewa 27 76 1984 10.1007/BF02192660 Cholewa PW: Remarks on the stability of functional equations. Aequationes Math 1984, 27: 76-86.
Abh Math Sem Univ Hamburg S Czerwik 62 59 1992 10.1007/BF02941618 Czerwik S: On the stability of the quadratic mapping in normed spaces. Abh Math Sem Univ Hamburg 1992, 62: 59-64.
J Diff Equ Appl C Park 12 1277 2006 10.1080/10236190600986925 Park C, Park J: Generalized Hyers-Ulam stability of an Euler-Lagrange type additive mapping. J Diff Equ Appl 2006, 12: 1277-1288.
Studia Univ Babeş-Bolyai Math ThM Rassias 43 89 1998 Rassias ThM: On the stability of the quadratic functional equation and its applications. Studia Univ Babeş-Bolyai Math 1998, 43: 89-124.
J Math Anal Appl ThM Rassias 246 352 2000 10.1006/jmaa.2000.6788 Rassias ThM: The problem of S.M. Ulam for approximately multiplicative mappings. J Math Anal Appl 2000, 246: 352-378.
J Math Anal Appl ThM Rassias 251 264 2000 10.1006/jmaa.2000.7046 Rassias ThM: On the stability of functional equations in Banach spaces. J Math Anal Appl 2000, 251: 264-284.
Glasnik Mat Ser III F Vajzović 2 22 73 1967 Vajzović F: Über das Funktional H mit der Eigenschaft: ( x, y ) = 0 ⇒ H ( x + y )+ H ( x - y ) = 2 H ( x ) + 2 H ( y ). Glasnik Mat Ser III 1967, 2(22):73-81.
Publ Inst Math (Beograd) F Drljević 54 63 1986 Drljević F: On a functional which is quadratic on A -orthogonal vectors. Publ Inst Math (Beograd) 1986, 54: 63-71.
Aequationes Math M Fochi 38 28 1989 10.1007/BF01839491 Fochi M: Functional equations in A -orthogonal vectors. Aequationes Math 1989, 38: 28-40.
J Diff Equ Appl MS Moslehian 11 999 2005 10.1080/10236190500273226 Moslehian MS: On the orthogonal stability of the Pexiderized quadratic equation. J Diff Equ Appl 2005, 11: 999-1004.
J Math Anal Appl MS Moslehian 318 211 2006 10.1016/j.jmaa.2005.05.052 Moslehian MS: On the stability of the orthogonal Pexiderized Cauchy equation. J Math Anal Appl 2006, 318: 211-223.
Aequationes Math Gy Szabó 40 190 1990 10.1007/BF02112295 Szabó Gy: Sesquilinear-orthogonally quadratic mappings. Aequationes Math 1990, 40: 190-200.
Aequa-tiones Math MS Moslehian 73 249 2007 10.1007/s00010-006-2868-0 Moslehian MS, Rassias ThM: Orthogonal stability of additive type equations. Aequa-tiones Math 2007, 73: 249-259.
Aequa-tiones Math L Paganoni 50 135 1995 10.1007/BF01831116 Paganoni L, Rätz J: Conditional function equations and orthogonal additivity. Aequa-tiones Math 1995, 50: 135-142.
J Inequal Pure Appl Math L Cădariu 4 1 7 2003 Cădariu L, Radu V: Fixed points and the stability of Jensen's functional equation. J Inequal Pure Appl Math 2003, 4(1):7. (Art. ID 4)
Bull Am Math Soc J Diaz 74 305 1968 10.1090/S0002-9904-1968-11933-0 Diaz J, Margolis B: A fixed point theorem of the alternative for contractions on a generalized complete metric space. Bull Am Math Soc 1968, 74: 305-309.
Int J Math Math Sci G Isac 19 219 1996 10.1155/S0161171296000324 Isac G, Rassias ThM: Stability of ψ -additive mappings: appications to nonlinear analysis. Int J Math Math Sci 1996, 19: 219-228.
Grazer Math Ber L Cădariu 346 43 2004 Cădariu L, Radu V: On the stability of the Cauchy functional equation: a fixed point approach. Grazer Math Ber 2004, 346: 43-52.
J Math Anal Appl Y Jung 306 752 2005 10.1016/j.jmaa.2004.10.017 Jung Y, Chang I: The stability of a cubic type functional equation with the fixed point alternative. J Math Anal Appl 2005, 306: 752-760.
Bull Braz Math Soc M Mirzavaziri 37 361 2006 10.1007/s00574-006-0016-z Mirzavaziri M, Moslehian MS: A fixed point approach to stability of a quadratic equation. Bull Braz Math Soc 2006, 37: 361-376.
Comput Math Appl R Saadati 60 2488 2010 10.1016/j.camwa.2010.08.055 Saadati R, Park C: Non-Archimedean ℒ-fuzzy normed spaces and stability of functional equations. Comput Math Appl 2010, 60: 2488-2496.
Math Commun R Saadati 16 131 2011 Saadati R, Vaezpour SM, Park C: The stability of the cubic functional equation in various spaces. Math Commun 2011, 16: 131-145.
Fixed Point Theory V Radu 4 91 2003 Radu V: The fixed point alternative and the stability of functional equations. Fixed Point Theory 2003, 4: 91-96.
J Math Anal Appl S Lee 307 387 2005 10.1016/j.jmaa.2004.12.062 Lee S, Im S, Hwang I: Quartic functional equations. J Math Anal Appl 2005, 307: 387-394.
J Math Anal Appl D MiheŢ 343 567 2008 10.1016/j.jmaa.2008.01.100 MiheŢ D, Radu V: On the stability of the additive Cauchy functional equation in random normed spaces. J Math Anal Appl 2008, 343: 567-572.
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