on the stability of an ๐‘š-variables functional equation in random normed spaces via fixed point method

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ID: 228662
2012
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Abstract
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.
Reference Key
ebadian2012discreteon Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;A. Ebadian;M. Eshaghi Gordji;H. Khodaei;R. Saadati;Gh. Sadeghi
Journal Journal of the American Heart Association
Year 2012
DOI
10.1155/2012/346561
URL
http://dx.doi.org/10.1155/2012/346561
Keywords
mathematics

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