Fixed point theorems of Rothe and Altman types about convex-power condensing operator and application (Q833159)

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 \(x(0)={\int}_0^Tb(s)x(s)\,ds\).