Fixed points of Lipschitzian semigroups in Banach spaces

Studia Mathematica (1997)

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

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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 $T={T}_{s}:C\to C:s\in G=\left[0,\infty \right)$ is a Lipschitzian semigroup such that $g=limin{f}_{G\ni \alpha \to \infty }in{f}_{G\ni \delta \ge 0}1/\alpha {ʃ}_{0}^{\alpha }\parallel {T}_{\beta +\delta }{\parallel }^{p}d\beta <1+c$, 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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