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 -