TY - JOUR
T1 - Common fixed points for pointwise Lipschitzian semigroups in modular function spaces
AU - Bin Dehaish, Buthinah A.
AU - Khamsi, Mohamed A.
AU - Kozlowski, Wojciech M.
N1 - Funding Information:
This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. (247-006-D1433). The authors, therefore, acknowledge with thanks technical and financial support of DSR.
PY - 2013/8
Y1 - 2013/8
N2 - Let C be a ρ-bounded, ρ-closed, convex subset of a modular function space Lρ. We investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups of nonlinear mappings T t : C → C, i.e. a family such that T0(f) = f, T s+t (f) = Ts o Tt(f) and ρ(T(f) - T(g)) ≤ αt (f)α(f - g), where lim sup t→∞αt (f) ≤ 1 for every f ∈ C. In particular, we prove that if Lρ is uniformly convex, then the common fixed point is nonempty ρ-closed and convex.
AB - Let C be a ρ-bounded, ρ-closed, convex subset of a modular function space Lρ. We investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups of nonlinear mappings T t : C → C, i.e. a family such that T0(f) = f, T s+t (f) = Ts o Tt(f) and ρ(T(f) - T(g)) ≤ αt (f)α(f - g), where lim sup t→∞αt (f) ≤ 1 for every f ∈ C. In particular, we prove that if Lρ is uniformly convex, then the common fixed point is nonempty ρ-closed and convex.
KW - Fixed point
KW - Modular function space
KW - Nonexpansive mapping
KW - Orlicz space
KW - Pointwise Lipschitzian mapping
KW - Pointwise nonexpansive mapping
KW - Semigroup
KW - Uniform convexity
UR - http://www.scopus.com/inward/record.url?scp=84902471725&partnerID=8YFLogxK
U2 - 10.1186/1687-1812-2013-214
DO - 10.1186/1687-1812-2013-214
M3 - Article
AN - SCOPUS:84902471725
SN - 1687-1820
VL - 2013
JO - Fixed Point Theory and Applications
JF - Fixed Point Theory and Applications
M1 - 214
ER -