TY - JOUR
T1 - Fixed point of asymptotic pointwise nonexpansive semigroups in metric spaces
AU - Al-Mezel, Saleh Abdullah
AU - Khamsi, Mohamed Amine
PY - 2013/8
Y1 - 2013/8
N2 - Let C be a bounded, closed, convex subset of a uniformly convex metric space (M, d). In this paper, we introduce the concept of asymptotic pointwise nonexpansive semigroups of nonlinear mappings Tt: C → C , i.e., a family such that T0 (x ) = x, Ts+t = Ts (Tt (x )), and d (Tt (x), Tt (y )) ≤ αt (x)d(x , y ), where lim supt →∞ αt (x) ≤ 1 for every x ∈ C . Then we investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups. The proof is based on the concept of types extended to one parameter family of points.
AB - Let C be a bounded, closed, convex subset of a uniformly convex metric space (M, d). In this paper, we introduce the concept of asymptotic pointwise nonexpansive semigroups of nonlinear mappings Tt: C → C , i.e., a family such that T0 (x ) = x, Ts+t = Ts (Tt (x )), and d (Tt (x), Tt (y )) ≤ αt (x)d(x , y ), where lim supt →∞ αt (x) ≤ 1 for every x ∈ C . Then we investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups. The proof is based on the concept of types extended to one parameter family of points.
KW - Fixed point
KW - Hyperbolic metric space
KW - Inequality
KW - Mann process
KW - Nearest point projection
KW - Nonexpansive mapping
KW - Semigroup
KW - Uniformly convex metric space
KW - Uniformly lipschitzian mapping
UR - http://www.scopus.com/inward/record.url?scp=84902578731&partnerID=8YFLogxK
U2 - 10.1186/1687-1812-2013-230
DO - 10.1186/1687-1812-2013-230
M3 - Article
AN - SCOPUS:84902578731
SN - 1687-1820
VL - 2013
JO - Fixed Point Theory and Applications
JF - Fixed Point Theory and Applications
M1 - 230
ER -