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Quadratic-Quartic Functional Equations in RN-Spaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2009Embargo end date: 01 Jan 2009 English Publisher:Springer Science and Business Media LLCJournal:Journal of Inequalities and Applications, volume 2,009, page 868,423 (issn: 1029-242X, Copyright policy )
Authors: Choonkil Park; M. Eshaghi Gordji; M. Bavand Savadkouhi;

doi: 10.1155/2009/868423 , 10.48550/arxiv.0903.1160

arXiv: http://arxiv.org/abs/0903.1160

Quadratic-Quartic Functional Equations in RN-Spaces

Abstract

In this paper, we obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary $t$-norms $$f(2x+y)+f(2x-y)=4[f(x+y)+f(x-y)]+2[f(2x)-4f(x)]-6f(y).$$

11 pages

Related Organizations
Keywords

Mathematics - Functional Analysis, 46S40, 39B72, 54E40., Applied Mathematics, QA1-939, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics, Analysis, Functional Analysis (math.FA)

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    influence
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
44
Average
Top 10%
Top 10%
Green
gold