Stability of an additive-quadratic-quartic functional equation

• Autorzy: Kim Gwang Hui , Lee Yang-Hi

Identyfikatory

DOI

10.1515/dema-2020-0001

• Języki publikacji: EN

Abstrakty

EN

In this paper, we investigate the stability of an additive-quadratic-quartic functional equation f(x+2y)+f(x-2y) - 2f(x+y) - 2f(-x-y) - 2f(x-y) - 2f(y-x)+4f(-x)+2f(x) - f(2y) - f(-2y)+4f(y)+4f(-y)=0 by the direct method in the sense of Găvruta.

Słowa kluczowe

EN

Hyers-Ulam stability; hyperstability; quadratic functional equation; fixed point theorem

PL

stabilność Hyersa-Ulama; hiperstabilność; równanie funkcyjne; twierdzenie o punkcie stałym

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2020
• Tom: Vol. 53, nr 1
• Strony: 1--7
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Kim Gwang Hui

• Department of Mathematics, Kangnam University, Yongin, Gyoenggi 16979, Republic of Korea

autor

Lee Yang-Hi

• Department of Mathematics Education, Gongju National University of Education, Gongju, 32553, Republic of Korea

Bibliografia

• [1] H. Azadi-Kenary, J.R. Lee, and C. Park, Non-Archimedean stability of an AQQ functional equation, J. Comput. Anal. Appl. 14 (2012), no. 2, 211–227.
• [2] M. Mohamadi, Y.J. Cho, C. Park, P. Vetro, and R. Saadati, Random stability of an additive-quadratic-quartic functional equation, J. Inequal. Appl. 2010 (2010), 754210, DOI: 10.1155/2010/754210.
• [3] C. Park, Fuzzy stability of an additive-quadratic-quartic functional equation, J. Inequal. Appl. 2010 (2010), 253040, DOI: 10.1155/2010/253040.
• [4] Y.-H. Lee, A fixed point approach to the stability of an additive-quadratic-quartic functional equation, Honam Mathematical J. (2019), accepted.
• [5] P. Găvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431–436.
• [6] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222–224.
• [7] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).