Approximate property of a functional equation with a general involution

• Autorzy: Bae J.-H. , Park W.-G.

Identyfikatory

DOI

10.1515/dema-2018-0021

• Języki publikacji: EN

Abstrakty

EN

In this paper, we prove the Hyers-Ulam stability of the functional equation f(x + y, z + w) + f(x + σ (y), z + τ(w)) = 2f(x, z) + 2f(y, w), where σ, τ are involutions.

Słowa kluczowe

EN

approximation; involution; Banach space

PL

aproksymacja; potęgowanie; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2018
• Tom: Vol. 51, nr 1
• Strony: 304--308
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Bae J.-H.

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

autor

Park W.-G.

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

Bibliografia

• [1] Ulam S. M., A Collection of Mathematical Problems, Interscience Publishers, New York, 1968
• [2] Hyers D. H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 1941, 27(4), 222–224
• [3] Aczél J., Dhombres J., Functional Equations in Several Variables, Cambridge Univ. Press, Cambridge, 1989
• [4] Brzdek J., Popa D., Rasa I., Xu B., Ulam Stability of Operators, A volume in Mathematical Analysis and its Applications, Academic Press, Elsevier, Oxford, 2018
• [5] El-fassi I., Brzdek J., Chahbi A., Kabbaj S., On hyperstability of the biadditive functional equation, Acta Math. Sci. Ser. B, 2017, 37(6), 1727–1739
• [6] Găvruta P., A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 1994, 184(3), 431–436
• [7] Jung S.-M., On the Hyers-Ulam Stability of the functional equations that have the quadratic property, J. Math. Anal. Appl., 1998, 222(1), 126–137
• [8] Bae J.-H., Park W.-G., A functional equation originating from quadratic forms, J. Math. Anal. Appl., 2007, 326(2), 1142–1148
• [9] Bae J.-H., Park W.-G., A functional equation originating from additive forms, (submitted)

Uwagi

PL

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