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

A. Ebadian, M. Eshaghi Gordji, H. Khodaei, R. Saadati and Gh. Sadeghi

Discrete Dynamics in Nature and Society, 2012, vol. 2012, 1-13

Abstract:

At first we find the solution of the functional equation ð · ð ‘“ ( ð ‘¥ 1 , … , ð ‘¥ ð ‘š ) ∶ = ∑ ð ‘š 𠑘 = 2 ( ∑ 𠑘 ð ‘– 1 = 2 ∑ 𠑘 + 1 ð ‘– 2 = ð ‘– 1 + 1 ⋯ ∑ ð ‘š ð ‘– ð ‘š − 𠑘 + 1 = ð ‘– ð ‘š − 𠑘 + 1 ) ð ‘“ ( ∑ ð ‘š ð ‘– = 1 , ð ‘– ≠𠑖 1 , … , ð ‘– ð ‘š − 𠑘 + 1 ð ‘¥ ð ‘– − ∑ ð ‘š − 𠑘 + 1 ð ‘Ÿ = 1 ð ‘¥ ð ‘– ð ‘Ÿ ) + ð ‘“ ( ∑ ð ‘š ð ‘– = 1 ð ‘¥ ð ‘– ) − 2 ð ‘š − 1 ð ‘“ ( ð ‘¥ 1 ) = 0 , where ð ‘š ≥ 2 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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:346561

DOI: 10.1155/2012/346561

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