... one of the important topics in the research differential equations, the boundary
value problem has attained a great deal of attention from many researchers, see 4–11 and the
references therein. ... class of four-point nonlocal boundary value
problem of nonlinear integrodifferential equations of fractional order by applying some fixed
point theorems.
On the...
... considered as the feasible set map. In the vector optimization problem corresponding
to each para meter valued x,ouraimistofindthesetofC-minimal point of the feasible set
map Gx.Theset-valuedmapW ... we mean the quantitative analysis,
that is, the study of derivatives of the perturbation function. On the other hand, by stability
we mean the qualitative analysis, that...
... the
x
i
(n)
2
values are sorted for 1 ≤ i ≤ K;
(2) the i values that determine the positions of 1 blocks
correspond to the N largest values of
x
i
(n)
2
.
3.2. The SPU-APA. The filter vector ... with M
= 8, K = 4, and N = 3, have
been presented for different values of σ
2
q
.Thedegreeof
nonstationary changes by selecting different values for σ
2
q
.As
we can see, for the...
... minimizer of VP. The set of all tightly
properly efficient solutions of VP is denoted by TPEVP.
In association with the vector optimization problem VP of set-valued maps, we
consider the following ... point of Lagrange
map L.
Proof. i By the necessity of Lemma 7.3,wehave
0
Y
∈ T
G
x
,
7.30
and there exists
y ∈ Fx such that x, y is a tightly properl...
... α<1. Then, the condition
ii of Theorem 2.1 is satisfied.
Let L
√
3/3, then the condition i of Theorem 2.1 is satisfied.
And
t
0
hsds
t
0
1.2/s 1ds 1.2lnt 1, then the condition ... Point Theory and Applications
Many authors have investigated the special cases of 1.1 and 1.2. Since Burton
1 used fixed point theory to investigate the stability of...
... implies the validity of condition ii in Theorem 3.1.
2 Advances in Difference Equations
As one of the focal topics in the research of dynamic equations on time scales, the study
of boundary value problems ... hybrid equations on various types of time scales 3–11. On the other hand, along
with the significant development of the theories, practical appl...
... part of the proof is similar to that of Theorem 3.3 a combined proof of
Theorems 3.1 and 3.2 and is therefore omitted.
By using the same methods as in the proof of Corollary 3.4, the following ... univalent in .
Furthermore, by using the same techniques as in the proof of Theorem 3.1,wecanprovethe
convexity univalence of F and so the details may be omitted. There...
... smaller the rotary speed and the larger the order, the
smaller the time spacing between adjacent order components
at the same frequency and the more liable the destruction
of the condition for the ... is to reconstruct the different or der components (or
harmonics) in the signal. There are three other conditions
for the convergence of the reconstructed order wav...
... contradicts the fact that
h<k. Hence the constant k in 3.1 is the best possible.
Thus we complete the proof of the theorem.
Journal of Inequalities and Applications 5
Setting y tx then
I
1
... and where the constant factors k and k
p
are the best
possibles.
Proof. If 2.13 takes the form of equality for some y ∈ −∞, 0 ∪ 0, ∞, then there exists
constants M a...
... In practice, the value of α
min
can be easily computed through a simple one
dimensional line search procedure over these two LMIs.
On the other hand, at the light of the results of Theorem 3.2, ... conditions of Theorem 3.2 are also satisfied with the same
controller and with the upper bounds γ
D
H2,ij
≤ γ
S
H2,ij
and γ
D
H∞,ij
≤ γ
S
H∞,ij
.
Proof. If the standard L...