On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces

Wojciech M. Kozlowski

On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces

Wojciech M. Kozlowski

Commentationes Mathematicae (2011)

Volume: 51, Issue: 1
ISSN: 2080-1211

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Abstract

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Let

C

be a

ρ

-bounded,

ρ

-closed, convex subset of a modular function space

L_{ρ}

. We investigate the existence of common fixed points for semigroups of nonlinear mappings

T_{t} : C \to C

, i.e. a family such that

T_{0} (x) = x

,

T_{s + t} = T_{s} (T_{t} (x))

, where each

T_{t}

is either

ρ

-contraction or

ρ

-nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.

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RIS

Wojciech M. Kozlowski. "On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces." Commentationes Mathematicae 51.1 (2011): null. <http://eudml.org/doc/291367>.

@article{WojciechM2011,
abstract = {Let $C$ be a $\rho $-bounded, $\rho $-closed, convex subset of a modular function space $L_\rho $. We investigate the existence of common fixed points for semigroups of nonlinear mappings $T_t\colon C\rightarrow C$, i.e. a family such that $T_0(x) = x$, $T_\{s+t\} = T_s (T_t (x))$, where each $T_t$ is either $\rho $-contraction or $\rho $-nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.},
author = {Wojciech M. Kozlowski},
journal = {Commentationes Mathematicae},
keywords = {Fixed point; common fixed point; nonexpansive mapping; contractions; semigroup of mappings; modular function space; modular space; Orlicz space; Musielak-Orlicz space},
language = {eng},
number = {1},
pages = {null},
title = {On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces},
url = {http://eudml.org/doc/291367},
volume = {51},
year = {2011},
}

TY - JOUR
AU - Wojciech M. Kozlowski
TI - On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces
JO - Commentationes Mathematicae
PY - 2011
VL - 51
IS - 1
SP - null
AB - Let $C$ be a $\rho $-bounded, $\rho $-closed, convex subset of a modular function space $L_\rho $. We investigate the existence of common fixed points for semigroups of nonlinear mappings $T_t\colon C\rightarrow C$, i.e. a family such that $T_0(x) = x$, $T_{s+t} = T_s (T_t (x))$, where each $T_t$ is either $\rho $-contraction or $\rho $-nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.
LA - eng
KW - Fixed point; common fixed point; nonexpansive mapping; contractions; semigroup of mappings; modular function space; modular space; Orlicz space; Musielak-Orlicz space
UR - http://eudml.org/doc/291367
ER -

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