An Extension of Darbo’s Theorem and Its Application

A. Samadi and M. B. Ghaemi

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Here, some extensions of Darbo fixed point theorem associated with measures of noncompactness are proved. Then, as an application, our attention is focused on the existence of solutions of the integral equation x(t) = F(t, f(t, x(α1(t)), x(α2(t))), ((Tx)(t)/Γ(α))×∫0t (u(t,s,max⁡[0,r(s)]⁡|x(γ1(τ))|, max⁡[0,r(s)]⁡|x(γ2(τ))|)/(t − s) 1−α)ds, ∫0∞v(t,s,x(t))ds), 0

Date: 2014
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https://doi.org/10.1155/2014/852324

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:852324

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