... T
2
x
0
.
Proof. Suppose that z
∈ T
2
C.Define
T
z
: T
z
x = T
1
x + z, ∀x ∈ C. (2.24)
FIXED POINT THEOREMS IN GENERATING SPACES OF
QUASI-NORM FAMILY AND APPLICATIONS
JIAN-ZHONG XIAO AND XING-HUA ZHU
Received ... case and in nonclassical case. In
this paper, we introduce some new concepts of generating spaces of quasi-norm family,
and establish some n...
... Fixed Point Theorems of
Functional Analysis (Tata Institute, Bombay, 1962) a proof by Singbal of the Schauder-
Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping
method, ... extension of Brouwer’s fixed point theorem to upper semi-
continuous set-valued mappings defined on compact convex subsets of
R
n
, which was
Hindawi Publishing Corporatio...
... 537–558.
[13] J. Reinermann and R. Sch
¨
oneberg, Some results and problems in the fixed point theory for non-
expansive and pseudocont ractive mappings in Hilbert-space, Fixed Point Theory and Its Ap-
plications ... continuous
mapping f : X → X has a fixed point.
Proof. For u,v ∈X we let [u,v] denote the (unique) met ric segment joining u and v and
let [u,v) = [u, v]\{v...
... TJ mapping of C into itself has a fixed point in C ;
(ii) C is bounded.
Proof. (i)⇒ (ii): Suppose that every asymptotic TJ mapping of C into itself has a fixed
point in C. Since the class of asymptotic ... mappings contain some important classes of
nonlinear mappings, like nonexpansive mappings and nonspreading mappings. We
prove fixed point theorems, ergodic theor...
... TJ mapping of C into itself has a fixed point in C ;
(ii) C is bounded.
Proof. (i)⇒ (ii): Suppose that every asymptotic TJ mapping of C into itself has a fixed
point in C. Since the class of asymptotic ... asymptotic nonspreading mapping of C into
itself has a fixed point in C.
3.5 Common fixed point theorems
Following the similar argument as the proof of Lem...
... Then
()(F
i
,T) has a point of coincidence,
()(F
j
,S) has a point of coincidence.
Moreover , (F
i
,T) has a common fixed point if T is quasi-coincidentally commuting and
coincidentally idempotent ... A.AhmadandM.Imdad,On common fixed point of mappings and multivalued mappings,Rad.
Mat. 8 (1992), no. 1, 147–158.
[2] , Some common fixed point theorems for mappings and m...
... results of fixed point theorems on CAT(0) spaces and Hilbert spaces.
Keywords: nonexpansive mapping, fixed point, generalized hybrid mapping, CAT(0)
spaces
1 Introduction
Fixed point theory in CAT(0) ... y)forallx, y Î C.A
point x Î C iscalledafixedpointofT if Tx = x.LetF(T)denotethesetoffixed
points of T.
Now, we introduce the following nonlinear mappings on CAT(...
... below).
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Fixed point theorems on ordered gauge spaces with applications to nonlinear
integral e...
... formatted
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Fixed point and weak convergence theorems for point- dependent lambda-hybrid
mappings in Banach spaces
Fixed Point Theory and Applications ... below).
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http://www.fixedpointtheoryandapplications.com...
... below).
For information about publishing your research in Fixed Point Theory and Applications go to
http://www.fixedpointtheoryandapplications.com/authors/instructions/
For information about other SpringerOpen ... uniqueness of fixed
point of T
N
, we have Tu = u. Thus, u is a fixed point of T . Since fixed point of
T is also fixed point of T
N
, we can conclude that T...