On the Stability of an 𝑚-Variables Functional Equation in Random Normed Spaces via Fixed Point Method
At first we find the solution of the functional equation 𝐷𝑓(𝑥1,…,𝑥𝑚)∶=∑𝑚𝑘=2(∑𝑘𝑖1=2∑𝑘+1𝑖2=𝑖1+1⋯∑𝑚𝑖𝑚−𝑘+1=𝑖𝑚−𝑘+1)𝑓(∑𝑚𝑖=1,𝑖≠𝑖1,…,𝑖𝑚−𝑘+1𝑥𝑖−∑𝑚−𝑘+1𝑟=1𝑥𝑖𝑟)+𝑓(∑𝑚𝑖=1𝑥𝑖)−2𝑚−1𝑓(𝑥1)=0, where 𝑚≥2 is an integer number. Then, we obtain the generalized Hyers-Ulam-Rassias stability in random normed spaces via the fix...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/346561 |