The stability of a cubic type functional equation with the fixed point alternative

By Yong-Soo Jung, Ick-Soon Chang. 2005

72 citations recorded by the source corpus.

Abstract In this note we investigate the generalized Hyers–Ulam–Rassias stability for the new cubic type functional equation f ( x + y + 2 z ) + f ( x + y − 2 z ) + f ( 2 x ) + f ( 2 y ) = 2 [ f ( x + y ) + 2 f ( x + z ) + 2 f ( x − z ) + 2 f ( y + z ) + 2 f ( y − z ) ] by using the fixed point alternative. The first systematic study of fixed point theorems in nonlinear analysis is due to G. Isac and Th.M. Rassias [Internat. J. Math. Math. Sci. 19 (1996) 219–228].

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/30f55eba8316d680ce696c4079ad288bf33d9b83

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In Applied Mathematics

1. Hamid Khodaei
2. Rassias Th.M.
3. Madjid Mirzavaziri
4. Mohammad Sal Moslehian
5. Janusz Brzdek
6. Choonkill Park
7. Krzysztof Cieplinski

In Mathematical Physics

1. Madjid Mirzavaziri
2. Mohammad Sal Moslehian
3. Rassias Th.M.
4. Hamid Khodaei
5. Krzysztof Cieplinski

Citations in the corpus

• A fixed point approach to stability of a quadratic equation (2005, methodology): “Using some ideas from [11, 19, 21, 22, 20, 4], we aim to use the alternative of fixed point theorem to establish the stability of this equation in the spirit of Hyers–Ulam under certain conditions.”
• Approximately generalized additive functions in several variables (2010, methodology): “Using such a clever idea, they could present a short, simple proof for the Hyers-Ulam stability of Cauchy and Jensen functional equations (see also [18, 40, 53]).”