Convexity of Solutions for an Iterative Equation in Banach Spaces

Xiaobing Gong

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: By applying Schauder′s fixed point theorem we investigate the existence of increasing (decreasing) solutions of the iterative equation ℋ(f)∘f = F and further give conditions under which those solutions are convex or concave. As corollaries we obtain results on iterative equation Gfx,fn1,…,fnkx=F(x) in Banach spaces, where n1, n2, …, nk ≥ 2.

Date: 2013
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https://doi.org/10.1155/2013/164851

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:164851

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