Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| < Np, where Np is n→ t s the normal structure coefficient of ...Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| < Np, where Np is n→ t s the normal structure coefficient of X. Suppose also there exists a nonempty bounded closed convex subset E of C with the following properties: (P1)x: E implies ωω(χ) C E; (P2)T is asymptotically regular on E. The authors prove that there exists a z E such that T(s)z = z for all s S. Fruther, under the similar condition, the existence of fixed points of Lipschitzian semigroups in a uniformly convex Banach space is discussed.展开更多
基金the National Natural Science Foundation of China (No.19801023) and theTeaching and Research Award Fund for Outstanding Young T
文摘Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| < Np, where Np is n→ t s the normal structure coefficient of X. Suppose also there exists a nonempty bounded closed convex subset E of C with the following properties: (P1)x: E implies ωω(χ) C E; (P2)T is asymptotically regular on E. The authors prove that there exists a z E such that T(s)z = z for all s S. Fruther, under the similar condition, the existence of fixed points of Lipschitzian semigroups in a uniformly convex Banach space is discussed.
