On Pexider Differences in Topological Vector Spaces

Abbas Najati, M. R. Abdollahpour and Gwang Hui Kim

Abstract and Applied Analysis, 2011, vol. 2011, 1-10

Abstract:

Let ð ‘‹ be a normed space and ð ‘Œ a sequentially complete Hausdorff topological vector space over the field â„š of rational numbers. Let ð · 1 = { ( ð ‘¥ , 𠑦 ) ∈ ð ‘‹ × ð ‘‹ ∶ ‖ ð ‘¥ ‖ + ‖ 𠑦 ‖ ≥ ð ‘‘ } , and ð · 2 = { ( ð ‘¥ , 𠑦 ) ∈ ð ‘‹ × ð ‘‹ ∶ ‖ ð ‘¥ ‖ + ‖ 𠑦 ‖ < ð ‘‘ } where ð ‘‘ > 0 . We prove that the Pexiderized Jensen functional equation is stable for functions defined on ð · 1 ( ð · 2 ) , and taking values in ð ‘Œ . We consider also the Pexiderized Cauchy functional equation.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:370104

DOI: 10.1155/2011/370104

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