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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 ${x}^{\text{'}}\left(t\right)=f\left(t,x\left(t\right)\right),\phantom{\rule{4pt}{0ex}}t\in \left[0,T\right]$, with the integral condition $x\left(0\right)={\int }_{0}^{T}b\left(s\right)x\left(s\right)\phantom{\rule{0.166667em}{0ex}}ds$.
##### MSC:
 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 47H09 Mappings defined by “shrinking” properties 47N20 Applications of operator theory to differential and integral equations 34G20 Nonlinear ODE in abstract spaces
##### References:
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