[理學院專題演講] 【01月03日】Adrian Petrusel / Fixed point theory for a special class of monotone orbital contractions in Hilbert spaces

Let H be a Hilbert space and T be a self monotone type operator on H. Under an appropriate condition, involving the Krasnoselskii operator generated by T (given by the convex combination of x and T(x)), we will prove a fixed point theorem for T, which generalize and complement several results in the theory of nonlinear operators. Some stability results are also proved and open questions are pointed out.