Fixed points of Lipschitzian semigroups in Banach spaces

Jarosław Górnicki

Studia Mathematica (1997)

  • Volume: 126, Issue: 2, page 101-113
  • ISSN: 0039-3223

Abstract

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We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If T = T s : C → C : s ∈ G = [ 0 , ∞ ) is a Lipschitzian semigroup such that g = l i m i n f G ∋ α → ∞ i n f G ∋ δ ≥ 0 1 / α ʃ 0 α ∥ T β + δ ∥ p d β < 1 + c , where c > 0 is some constant, then there exists x ∈ C such that T s x = x for all s ∈ G.

How to cite

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Górnicki, Jarosław. "Fixed points of Lipschitzian semigroups in Banach spaces." Studia Mathematica 126.2 (1997): 101-113. <http://eudml.org/doc/216446>.

@article{Górnicki1997,
abstract = {We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If $T = \{T_s: C → C: s ∈ G = [0,∞)\}$ is a Lipschitzian semigroup such that $g = lim inf_\{G ∋ α → ∞\} inf_\{G ∋ δ ≥ 0\} 1/α ʃ^α_0 ∥T_\{β+δ\}∥^p dβ < 1 + c$, where c > 0 is some constant, then there exists x ∈ C such that $T_sx = x$ for all s ∈ G.},
author = {Górnicki, Jarosław},
journal = {Studia Mathematica},
keywords = {Lipschitzian semigroup; fixed point; p-uniformly convex Banach space},
language = {eng},
number = {2},
pages = {101-113},
title = {Fixed points of Lipschitzian semigroups in Banach spaces},
url = {http://eudml.org/doc/216446},
volume = {126},
year = {1997},
}

TY - JOUR
AU - Górnicki, Jarosław
TI - Fixed points of Lipschitzian semigroups in Banach spaces
JO - Studia Mathematica
PY - 1997
VL - 126
IS - 2
SP - 101
EP - 113
AB - We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If $T = {T_s: C → C: s ∈ G = [0,∞)}$ is a Lipschitzian semigroup such that $g = lim inf_{G ∋ α → ∞} inf_{G ∋ δ ≥ 0} 1/α ʃ^α_0 ∥T_{β+δ}∥^p dβ < 1 + c$, where c > 0 is some constant, then there exists x ∈ C such that $T_sx = x$ for all s ∈ G.
LA - eng
KW - Lipschitzian semigroup; fixed point; p-uniformly convex Banach space
UR - http://eudml.org/doc/216446
ER -

References

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