Hyers-Ulam stability of quadratic forms in 2-normed spaces

• Autorzy: Park Won-Gil , Bae Jae-Hyeong

Identyfikatory

DOI

10.1515/dema-2019-0038

• Języki publikacji: EN

Abstrakty

EN

In this paper, we obtain Hyers-Ulam stability of the functional equations f(x+y, z+w) + f(x-y, z-w) = 2f(x, z) + 2f(y, w), f(x+y, z-w) + f(x-y, z+w) = 2f(x, z) + 2f(y, w) and f(x+y, z-w) + f(x-y, z+w) = 2f(x, z) - 2f(y, w) in 2-Banach spaces. The quadratic forms ax2+bxy+cy2, ax2+by2 and axy are solutions of the above functional equations, respectively.

Słowa kluczowe

EN

linear 2-normed space; quadratic form; Hyers-Ulam stability

PL

przestrzeń unormowana; przestrzeń linearna; forma kwadratowa; stabilność Hyersa-Ulama

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 496--502
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Park Won-Gil

• Department of Mathematics Education, College of Education, Mokwon University, Daejeon 35349, Republic of Korea

autor

Bae Jae-Hyeong

• Humanitas College, Kyung Hee University, Yongin 17104, Republic of Korea

Bibliografia

• [1] Gähler S., 2-metrische Räume und ihre topologische Struktur, Math. Nachr., 1963, 26, 115-148
• [2] Gähler S., Lineare 2-normierte Räumen, Math. Nachr., 1964, 28, 1-43
• [3] Chu H.-Y., Kim A., Park J., On the Hyers-Ulam stabilities of functional equations on n-Banach spaces, Math. Nachr., 2016, 289(10), 1177-1188
• [4] Ulam S. M., A Collection of Mathematical Problems, Interscience Publishers, New York, 1960
• [5] Hyers D. H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci., 1941, 27, 222-224
• [6] Rassias Th. M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 1978, 72, 297-300
• [7] Bae J.-H., Park W.-G., A functional equation originating from quadratic forms, J. Math. Anal. Appl., 2007, 326, 1142-1148
• [8] Park W.-G., Bae J.-H., A functional equation related to quadratic forms without the cross product terms, Honam Math. J., 2008, 30, 219-225
• [9] Park W.-G., Bae J.-H., Stability of a bi-additive functional equation in Banach modules over a C*-algebra, Discrete Dyn. Nat. Soc., 2012, Article ID 835893
• [10] Park W.-G., Approximate additive mappings in 2-Banach spaces and related topics, J. Math. Anal. Appl., 2011, 376, 193-202

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).