On the Stability of an 𝑚-Variables Functional Equation in Random Normed Spaces via Fixed Point Method

On the Stability of an ๐‘š-Variables Functional Equation in Random Normed Spaces via Fixed Point Method

At first we find the solution of the functional equation ๐ท๐‘“(๐‘ฅ1,โ€ฆ,๐‘ฅ๐‘š)โˆถ=โˆ‘๐‘š๐‘˜=2(โˆ‘๐‘˜๐‘–1=2โˆ‘๐‘˜+1๐‘–2=๐‘–1+1โ‹ฏโˆ‘๐‘š๐‘–๐‘šโˆ’๐‘˜+1=๐‘–๐‘šโˆ’๐‘˜+1)๐‘“(โˆ‘๐‘š๐‘–=1,๐‘–โ‰ ๐‘–1,โ€ฆ,๐‘–๐‘šโˆ’๐‘˜+1๐‘ฅ๐‘–โˆ’โˆ‘๐‘šโˆ’๐‘˜+1๐‘Ÿ=1๐‘ฅ๐‘–๐‘Ÿ)+๐‘“(โˆ‘๐‘š๐‘–=1๐‘ฅ๐‘–)โˆ’2๐‘šโˆ’1๐‘“(๐‘ฅ1)=0, where ๐‘šโ‰ฅ2 is an integer number. Then, we obtain the generalized Hyers-Ulam-Rassias stability in random normed spaces via the fix...

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Bibliographic Details
Main Authors: A. Ebadian, M. Eshaghi Gordji, H. Khodaei, R. Saadati, Gh. Sadeghi
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2012/346561
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Summary:At first we find the solution of the functional equation ๐ท๐‘“(๐‘ฅ1,โ€ฆ,๐‘ฅ๐‘š)โˆถ=โˆ‘๐‘š๐‘˜=2(โˆ‘๐‘˜๐‘–1=2โˆ‘๐‘˜+1๐‘–2=๐‘–1+1โ‹ฏโˆ‘๐‘š๐‘–๐‘šโˆ’๐‘˜+1=๐‘–๐‘šโˆ’๐‘˜+1)๐‘“(โˆ‘๐‘š๐‘–=1,๐‘–โ‰ ๐‘–1,โ€ฆ,๐‘–๐‘šโˆ’๐‘˜+1๐‘ฅ๐‘–โˆ’โˆ‘๐‘šโˆ’๐‘˜+1๐‘Ÿ=1๐‘ฅ๐‘–๐‘Ÿ)+๐‘“(โˆ‘๐‘š๐‘–=1๐‘ฅ๐‘–)โˆ’2๐‘šโˆ’1๐‘“(๐‘ฅ1)=0, where ๐‘šโ‰ฅ2 is an integer number. Then, we obtain the generalized Hyers-Ulam-Rassias stability in random normed spaces via the fixed point method for the above functional equation.
ISSN:1026-0226
1607-887X

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