Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces

Abstract

Fixed point theorems for generalized Lipschitzian semigroups are proved in p-uniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp, and in Sobolev spaces Hk,p, for 1<p<∞ and k≥0.

Keywords

• Semitopological semigroup
• submean
• generalized Lipschitzian semigroup
• p-uniformly convex Banach space
• uniformly normal structure.