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      Stability of a mixed quadratic and additive functional equation in quasi-Banach spaces

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      https://www.riss.kr/link?id=A103867929

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      다국어 초록 (Multilingual Abstract)

      In this paper we establish the general solution of the functional equation f(2x + y) + f(x − 2y) = 2f(x + y) + 2f(x− y) + f(−x) + f(−y) and investigate the Hyers–Ulam–Rassias stability of this equation in quasi- Banach spaces. The conc...

      In this paper we establish the general solution of the functional
      equation
      f(2x + y) + f(x − 2y) = 2f(x + y) + 2f(x− y) + f(−x) + f(−y)
      and investigate the Hyers–Ulam–Rassias stability of this equation in quasi-
      Banach spaces. The concept of Hyers-Ulam-Rassias stability originated
      from Th. M. Rassias’ stability theorem that appeared in his paper: On the
      stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.
      72 (1978), 297–300.

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      다국어 초록 (Multilingual Abstract)

      In this paper we establish the general solution of the functional equation f(2x + y) + f(x − 2y) = 2f(x + y) + 2f(x− y) + f(−x) + f(−y) and investigate the Hyers–Ulam–Rassias stability of this equation in quasi- Banach spaces. The concept ...

      In this paper we establish the general solution of the functional
      equation
      f(2x + y) + f(x − 2y) = 2f(x + y) + 2f(x− y) + f(−x) + f(−y)
      and investigate the Hyers–Ulam–Rassias stability of this equation in quasi-
      Banach spaces. The concept of Hyers-Ulam-Rassias stability originated
      from Th. M. Rassias’ stability theorem that appeared in his paper: On the
      stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.
      72 (1978), 297–300.

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      참고문헌 (Reference)

      1 Th.M. Rassias, "What is left of Hyers–Ulam stabilirty?" 1 : 65-69, 1992

      2 S.-M. Jung, "Ulam’s problem for approximate homomorphisms in connection with Bernoulli’s differential equation" 187 : 223-227, 2007

      3 K. Jun, "Ulam stability problem for a mixed type of cubic and additive functional equation" 13 : 271-285, 2006

      4 Th.M.Rassias, "Topics in Mathematical Analysis" World Scientific Publishing Co 1989

      5 V.A. Faizev, "The space of ( , )-additive mappings on semigroups" 354 (354): 4455-4472, 2002

      6 A. Grabiec, "The generalized Hyers-Ulam stability of a class of functional equations" 48 : 217-235, 1996

      7 C. Park, "Stability of functional inequalities associated with Jordanvon Neumann type additive functional equations" 2007

      8 M.S. Moslehian, "Stability of functional equations in Non-Archimedean spaces" 1 : 325-334, 2007

      9 A. Najati, "Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spaces" 337 : 399-415, 2008

      10 Th.M. Rassias, "Stability of Mappings of Hyers–Ulam Type" Hadronic Press Inc 1994

      1 Th.M. Rassias, "What is left of Hyers–Ulam stabilirty?" 1 : 65-69, 1992

      2 S.-M. Jung, "Ulam’s problem for approximate homomorphisms in connection with Bernoulli’s differential equation" 187 : 223-227, 2007

      3 K. Jun, "Ulam stability problem for a mixed type of cubic and additive functional equation" 13 : 271-285, 2006

      4 Th.M.Rassias, "Topics in Mathematical Analysis" World Scientific Publishing Co 1989

      5 V.A. Faizev, "The space of ( , )-additive mappings on semigroups" 354 (354): 4455-4472, 2002

      6 A. Grabiec, "The generalized Hyers-Ulam stability of a class of functional equations" 48 : 217-235, 1996

      7 C. Park, "Stability of functional inequalities associated with Jordanvon Neumann type additive functional equations" 2007

      8 M.S. Moslehian, "Stability of functional equations in Non-Archimedean spaces" 1 : 325-334, 2007

      9 A. Najati, "Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spaces" 337 : 399-415, 2008

      10 Th.M. Rassias, "Stability of Mappings of Hyers–Ulam Type" Hadronic Press Inc 1994

      11 D.H. Hyers, "Stability of Functional Equations in Several Variables" Birkh¨auser 1998

      12 P.W. Cholewa, "Remarks on the stability of functional equations" 27 : 76-86, 1984

      13 Pl. Kannappan, "Quadratic functional equation and inner product spaces" 27 : 368-372, 1995

      14 S. Czerwik, "On the stability of the quadratic mapping in normed spaces" 62 : 59-64, 1992

      15 Th.M. Rassias, "On the stability of the linear mapping in Banach spaces" 72 : 297-300, 1978

      16 C. Park, "On the stability of the linear mapping in Banach modules" 275 : 711-720, 2002

      17 D. H. Hyers, "On the stability of the linear functional equation" 27 : 222-224, 1941

      18 Th.M. Rassias, "On the stability of functional equations and a problem of Ulam" 62 (62): 23-130, 2000

      19 A. Najati, "On the stability of a quartic functional equation" 340 : 569-574, 2008

      20 K. Jun, "On the Hyers–Ulam–Rassias stability of a Pexiderized quadratic inequality" 4 : 93-118, 2001

      21 G. Isac, "On the Hyers–Ulam stability of -additive mappings" 72 : 131-137, 1993

      22 P. Jordan, "On inner products in linear metric spaces" 36 : 719-723, 1935

      23 J.M. Rassias, "On approximation of approximately linear mappings by linear mappings" 46 : 126-130, 1982

      24 박춘길, "On a Generalized Trif's Mapping in Banach Modules over a$C^*$-Algebra" 대한수학회 43 (43): 323-356, 2006

      25 H. Haruki, "New generalizations of Jensen’s functional equation" 123 : 495-503, 1995

      26 S. Rolewicz, "Metric Linear Spaces" PWN-Polish Sci. Publ 1984

      27 F. Skof, "Local properties and approximations of operators" 53 : 113-129, 1983

      28 C. Park, "Isomorphisms Between Quasi-Banach Algebras" 28 (28): 353-362, 2007

      29 C. Park, "Isometric additive mappings in quasi-Banach spaces" 12 (12): 377-385, 2007

      30 C. Park, "Hyers–Ulam–Rassias stability of homomorphisms in quasi-Banach algebras" 2006

      31 S.-M. Jung, "Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis" Hadronic Press lnc 2001

      32 A. Najati, "Hyers–Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation" 335 : 763-778, 2007

      33 A. Najati, "Hyers–Ulam Stability of an n-Apollonius type Quadratic Mapping" 14 (14): 755-774, 2007

      34 C. Park, "Homomorphisms and derivations in proper JCQ -triples" 337 : 1404-1414, 2008

      35 Y. Benyamini, "Geometric Nonlinear Functional Analysis" Colloq.Publ 2000

      36 C. Baak, "Generalized additive mapping in Banach modules and isomorphisms between C -algebras" 314 : 150-161, 2006

      37 Th.M. Rassias, "Functional Equations, Inequalities and Applications" Kluwer Academic Publishers Co 2003

      38 J. Acz´el, "Functional Equations in Several Variables" Cambridge University Press 1989

      39 P. Czerwik, "Functional Equations and Inequalities in Several Variables" World Scientific Publishing Company 2002

      40 Th.M.Rassias, "Functional Equations and Inequalities" Kluwer Academic Publishers 2000

      41 D. Amir, "Characterizations of Inner Product Spaces" Birkh¨auser 1986

      42 D.H. Hyers, "Approximate homomorphisms" 44 : 125-153, 1992

      43 K. Jun, "A generalization of the Hyers–Ulam–Rassias stability of the Pexiderized quadratic equations" 297 : 70-86, 2004

      44 P. G˘avruta, "A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings" 184 : 431-436, 1994

      45 S.M. Ulam, "A Collection of the Mathematical Problems" Interscience Publ 1960

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      연월일 이력구분 이력상세 등재구분
      2026 평가예정 재인증평가 신청대상 (재인증)
      2020-01-01 평가 등재학술지 유지 (재인증) KCI등재
      2019-11-08 학회명변경 영문명 : The Korean Society For Computational & Applied Mathematics And Korean Sigcam -> Korean Society for Computational and Applied Mathematics KCI등재
      2017-01-01 평가 등재학술지 유지 (계속평가) KCI등재
      2013-01-01 평가 등재학술지 유지 (등재유지) KCI등재
      2010-01-01 평가 등재학술지 유지 (등재유지) KCI등재
      2008-02-18 학술지명변경 한글명 : Journal of Applied Mathematics and Infomatics(Former: Korean J. of Comput. and Appl. Math.) -> Journal of Applied Mathematics and Informatics
      외국어명 : Journal of Applied Mathematics and Infomatics(Former: Korean J. of Comput. and Appl. Math.) -> Journal of Applied Mathematics and Informatics
      KCI등재
      2008-02-15 학술지명변경 한글명 : Journal of Applied Mathematics and Computing(Former: Korean J. of Comput. and Appl. Math.) -> Journal of Applied Mathematics and Infomatics(Former: Korean J. of Comput. and Appl. Math.)
      외국어명 : Journal of Applied Mathematics and Computing(Former: Korean J. of Comput. and Appl. Math.) -> Journal of Applied Mathematics and Infomatics(Former: Korean J. of Comput. and Appl. Math.)
      KCI등재
      2008-01-01 평가 등재학술지 유지 (등재유지) KCI등재
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      2001-01-01 평가 등재학술지 선정 (등재후보2차) KCI등재
      1998-07-01 평가 등재후보학술지 선정 (신규평가) KCI등재후보
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      기준연도 WOS-KCI 통합IF(2년) KCIF(2년) KCIF(3년)
      2016 0.16 0.16 0.13
      KCIF(4년) KCIF(5년) 중심성지수(3년) 즉시성지수
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