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2015 | 29 | 1 | 35-50
Tytuł artykułu

Mixed Type Of Additive And Quintic Functional Equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form [...] f(3x+y)−5f(2x+y)+f(2x−y)+10f(x+y)−5f(x−y)=10f(y)+4f(2x)−8f(x) $$f\left( {3x + y} \right) - 5f\left( {2x + y} \right) + f\left( {2x - y} \right) + 10f\left( {x + y} \right) - 5f\left( {x - y} \right) = 10f\left( y \right) + 4f\left( {2x} \right) - 8f\left( x \right)$$ in the set of real numbers.
Wydawca
Rocznik
Tom
29
Numer
1
Strony
35-50
Opis fizyczny
Daty
wydano
2015-09-01
otrzymano
2014-07-17
poprawiono
2014-10-31
online
2015-09-30
Twórcy
  • Department of Mathematics, Thiruvalluvar University College of Arts and Science, Gazhalnayaganpatti, Tirupattur-635 901 Tamil Nadu, India, drpnarasimman@gmail.com
  • Department of Mathematics, Sacred Heart College, Tirupattur-635 601, TamilNadu, India, shckravi@yahoo.co.in
  • Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran, shoujaei@kiau.ac.ir
Bibliografia
  • [1] Aoki T., On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2 (1950), 64–66.[Crossref]
  • [2] Bodaghi A., Quintic functional equations in non-Archimedean normed spaces, J. Math. Extension 9 (2015), no. 3, 51–63.
  • [3] Bodaghi A., Moosavi S.M., Rahimi H., The generalized cubic functional equation and the stability of cubic Jordan *-derivations, Ann. Univ. Ferrara 59 (2013), 235–250.[Crossref]
  • [4] Cădariu L., Radu V., Fixed points and the stability of quadratic functional equations, An. Univ. Timişoara, Ser. Mat. Inform. 41 (2003), 25–48.
  • [5] Cădariu L., Radu V., On the stability of the Cauchy functional equation: A fixed point approach, Grazer Math. Ber. 346 (2004), 43–52.
  • [6] Czerwik S., On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg. 62 (1992), 59–64.[Crossref]
  • [7] Hyers D.H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA. 27 (1941), 222–224.[Crossref]
  • [8] Hyers D.H., Isac G., Rassias Th.M., Stability of functional equations in several variables, Birkhauser, Boston, 1998.
  • [9] Jung S.-M., Hyers–Ulam–Rassias stability of functional equations in nonlinear analysis, Springer, New York, 2011.
  • [10] Kannappan P., Functional equations and inequalities with applications, Springer, New York, 2009.
  • [11] Najati A., Moghimi M.B., Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spaces, J. Math. Anal. Appl. 337 (2008), 339–415.
  • [12] Park C., Cui J., Eshaghi Gordji M., Orthogonality and quintic functional equations, Acta Math. Sinica, English Series 29 (2013), 1381–1390.[Crossref]
  • [13] Rassias J.M., On approximation of approximately linear mappings by linear mapping, J. Funct. Anal. 46 (1982), no. 1, 126–130.[Crossref]
  • [14] Rassias J.M., On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math. (2) 108 (1984), no. 4, 445–446.
  • [15] Rassias Th.M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.[Crossref]
  • [16] Rassias Th.M., Brzdęk J., Functional equations in mathematical analysis, Springer, New York, 2012.
  • [17] Ulam S.M., Problems in modern mathematics, Chapter VI, Science Ed., Wiley, New York, 1940.
  • [18] Xu T.Z., Rassias J.M., Rassias M.J., Xu W.X., A fixed point approach to the stability of quintic and sextic functional equations in quasi-β-normed spaces, J. Inequal. Appl. (2010), Article ID 423231, 23 pp, doi:10.1155/2010/423231.[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_amsil-2015-0004
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