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Fixed point theorems of Rothe and Altman types about convex-power condensing operator and application. (English) Zbl 1183.47054

Fixed point theorems of Rothe and Altman type are given for convex-power condensing operators on a general Banach space. As an application, an existence result is derived for the equation \(x^{\prime}(t) = f(t,x(t)), \;t\in [0,T]\), with the integral condition \(x(0)={\int}_0^Tb(s)x(s)\,ds\).

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47N20 Applications of operator theory to differential and integral equations
34G20 Nonlinear differential equations in abstract spaces
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