Báo cáo hóa học: "Research Article T -Stability of Picard Iteration in Metric Spaces" pot
Báo cáo hóa học: "Research Article T -Stability of Picard Iteration in Metric Spaces" pot
... Kirk, or any other
iteration scheme since, if one obtains convergence to a fixed point for a map using Picard s
iteration, there is no point in considering any other more complicated iteration procedure.
Acknowledgment
This ... 5
Then, Picard s iteration is T- stable.
Proof. From 2, Theorem 11, T has a unique fixed point q. Also, T satisfies 1. It remains to
show that 2 i...
Báo cáo hóa học: " Research Article T -Stability of Picard Iteration in Metric Spaces" potx
... sufficient conditions that Picard s iteration is T- stable for an arbitrary
self-map, and then demonstrate that a number of contractive conditions are Picard T- stable.
We will need the following lemma ... is not bounded, then it cannot
possibly converge. If these conditions hold for x
n1
Tx
n
, that is, Picard s iteration, then we
will say that Picard s iteration is T- stable...
Báo cáo hóa học: " Research Article A Generalisation of Contraction Principle in Metric Spaces" pot
... of the concept of altering distance function. It has also been extended in
the context of multivalued 14 and fuzzy mappings 15. The concept of altering distance
function has also been introduced ... equivalently dz
1
,z
2
0, that is, z
1
z
2
.
This proves the uniqueness of the fixed point.
If we particularly take φ t 1 − kψ t t& gt;0 where 0 <k<1, then we obtain t...
Báo cáo hóa học: " Research Article General Convexity of Some Functionals in Seminormed Spaces and Seminormed Algebras" pdf
... prove that ρ
n
p, x ≥ γ.Inviewofthefact
that was mentioned at the beginning, we get ρ
2
p, xδα, t ≥ γ. Assuming the statement
for n − 1 holds, we will prove it for n.
1 Let k ≤ 2.
Putting ... hence, α · t β /t p
p−1
−1
.
Further, we obtain t βp
p−1
−1
− α
−1
. It is obvious that we have a minimum at this point in
the interval 0, 1.
Then, we obtain 1/α · t...
Báo cáo hóa học: " Research Article Determining Number of Independent Sources in Undercomplete Mixture" potx
... on the maximisation of joint entropy of the output
and using correlation between output and input to recover
the ICs for undercomplete situation. This technique is an
iterative approach that minimises ... comparison of
this approach with the rank, R,ofG indicates that R is not
suitable for estimating N. The results also indicate that there
is a significant improvement of quality of s...
Báo cáo hóa học: " Research Article Common Fixed Points for Multimaps in Metric Spaces" doc
... particular the fixed point set of f and the fixed point
set of g intersect. The rest of the proof is similar to that of Esp
´
ınola and Kirk 24, Theorem
4.3 and so is omitted.
In the next result, we ... convexity of the values of T but,
this time, we ask the geodesic space M not to have bifurcating geodesics. That is, for any two
segments starting at the same point and having...
Báo cáo hóa học: " Research Article Lyapunov Stability of Quasilinear Implicit Dynamic Equations on Time Scales" docx
... A
t
−
B
t
T
t
Q
t
. It is easy to see that
T
t
Q
t
G
−1
t
G
t
T
t
Q
t
G
−1
t
A
t
− B
t
T
t
Q
t
T
t
Q
t
P
t
− T
t
Q
t
G
−1
t
B
t
T
t
Q
t
T
t
Q
t
T
t
Q
t
T
t
Q
t
. ... 2.11. Finally,
Q
t
G
−1
t
B
t
Q
t
G
−1
t
B
t
P
ρ t
Q
t
G
−1
t
B
t
T
t
Q
t
T
−1
t
Q
ρ t
Q
t
G
−1...
Báo cáo hóa học: " Research Article Lagrangian Stability of a Class of Second-Order Periodic Systems" docx
... all time, that is, whether there are resonances that might cause the amplitude
of the oscillations to increase without bound.
The first positive result of boundedness of solutions in the superlinear ... Problems
2. The Proof of Theorem
The proof of Theorem 1.1 is based on Moser’s small twist theorem for reversible mapping. It
mainly consists of two steps. The first one is to find a...
báo cáo hóa học:" Research Article Exponential Stability of Two Coupled Second-Order Evolution Equations" pptx
... exponentially. An example is give to illustrate that the result obtained
can be applied to concrete partial differential equations.
1. Introduction
Of concern is the exponential stability of two ...
T
S
√
Av t βu t
2
dt.
2.28
Proof. Taking the inner product of both sides of 1.2 with v t and integrating over S, T ,
we see
T
S
v
t
2
dt
T...
Báo cáo hóa học: " Research Article Fuzzy Stability of the Pexiderized Quadratic Functional Equation: A Fixed Point Approach" doc
... properly cited.
1. Introduction
The aim of this article is to extend the applications of the fixed point alternative method to
provide a fuzzy version of Hyers-Ulam-Rassias stability for the functional ... Applications
The uniqueness of T follows from the fact that T is the unique fixed point of J
1
with
the property that there exists k ∈ 0, ∞ such that
N
T
x
− f
x
...