A fixed point approach to the stability of an AQCQ-functional equation in RN-spaces

Volume 9, Issue 4, pp 1787--1806 http://dx.doi.org/10.22436/jnsa.009.04.34

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Authors

Choonkil Park - Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea. Dong Yun Shin - Department of Mathematics, University of Seoul, Seoul 130-743, Republic of Korea. Sungjin Lee - Department of Mathematics, Daejin University, Kyeonggi 487-711, Republic of Korea.

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of the following additive-quadratic- cubic-quartic functional equation \[f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f(-2y) - 4f(y) - 4f(-y)\] in random normed spaces.

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Keywords

• Random normed space
• fixed point
• Hyers-Ulam stability
• additive-quadratic-cubic-quartic functional equation.

MSC

•  39B52
•  54E70
•  47H10
•  54E40.

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