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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 ' (t)=f(t,x(t)),t[0,T], with the integral condition x(0)= 0 T b(s)x(s)ds.
MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
47N20Applications of operator theory to differential and integral equations
34G20Nonlinear ODE in abstract spaces
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