Báo cáo hóa học: " Research Article Functional Equation f x Its Hyers-Ulam Stability" potx
Báo cáo hóa học: " Research Article Functional Equation f x Its Hyers-Ulam Stability" potx
... easily verify that
f
x
− af
x −
1
b
n
f
x − n
− af
x − n − 1
,
f
x
− bf
x − 1
a
n
f
x − n
− bf
x − n − 1
2.3
for all x ∈ R and n ∈{0, 1, 2, }. If we substitute ... qU
x
h
x −
x
− 1
,
f
x − 1
U
x
h
x −
x
− qU
x
−1
h
x −
x
− 1
,
f
x − 2
U
x
−1
h...
Báo cáo hóa học: "Research Article A Fixed Point Approach to the Stability of a Functional Equation of the Spiral of Theodorus" pptx
... −
1
i
√
x 1
f x
≤ ϕ x 3.2
for all x ≥ a, then there exists a unique solution F : a, ∞ →
C of 1.1, which satisfies
F x − f x
≤
1
1 − L
ϕ x 3.3
for all x ≥ a. More ... 1
n
k1
−i
k1
1j
1
≤···≤j
k1
≤n1−k
×
k1
m1
1
x j
m
f x n − k −
i
√
x 1
f x n
Λ
n
f
x 1
n−1
k1
−i
k1
1j
1
≤···≤j
k1
≤n1−k...
Báo cáo hóa học: " Research Article Functional Classification of Genome-Scale Metabolic Networks" potx
... principle, by its stoichiometry, able to produce if
exactly the seed compounds are available. By the inclusion
of cofactor functionality (see methods for details), the
interpretation of a scope as ... pestis_Mediaevails
P. atlantica
X. oryzae
X. campestris_vesicatoria
X. axonopodis
X. campestris_B
X. campestris
P. fluorescens_PfO1
P. putida
P. entomophila
P. aeruginosa
P. fluorescens
H...
Báo cáo hóa học: " Research Article Fixed Point Methods for the Generalized Stability of Functional Equations in a Single Variable" ppt
... 4.16
where
J
n
f
x F
x,
J
n−1
f
η x
F
x, F
η x ,
J
n−2
f
η x
, x ∈ G,
4.17
hence
J
n
f
x F
x, F
F
η x , F
η x ,
f ◦ η
n
η x
. 4.18
iii ρ f, c ≤ ... the equation
c x F
x, c
η x
, x ∈ G, 4.5
and the estimation
d
f x ,c x
≤
ψ x
1 − L
, x ∈ G. 4.6
Moreover,
c x lim
n→∞
F
x,...
Báo cáo hóa học: " Research Article Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras" docx
... z), (3.3)
f (xyz) − f (xy)z + xf(y)z − xf(yz)
A
≤ ϕ (x, y, z) (3.4)
for all x, y,z
∈ A.IfthereexistsanL<1 such that ϕ (x, x ,x) ≤ 2Lϕ (x/ 2 ,x/ 2 ,x/ 2) for all
x
∈ A and if f (tx) is continuous ... (2.2)
Cf (x, y,z)
B
≤ ϕ (x, y,z), (2.3)
f (xy) − f (x) f (y)
B
≤ ϕ (x, y, 0) (2.4)
for all x, y,z
∈ A.IfthereexistsanL<1 such that ϕ (x, x ,x) ≤ 2Lϕ (...
Báo cáo hóa học: " Research Article A Fixed Point Approach to the Stability of a Volterra Integral Equation" pptx
... the
inequality
f (x + y) − f (x) − f (y)≤ε,forallx and y, can be approximated by an exact
solution, say an additive function. In this case, the Cauchy additive functional equation,
f (x + y)
= f (x) + f (y), ... generalized metric on X if and only if d satisfies
the following:
(M
1
) d (x, y) = 0ifandonlyifx = y;
(M
2
) d (x, y) = d(y, x) forallx, y ∈ X;
(M
3
) d (x, z...
Báo cáo hóa học: " Research Article Functional Inequalities Associated with Jordan-von Neumann-Type Additive Functional " potx
... = x in (5.1), we get
f ( 2x) + 2f ( x)
Y
1+2
r
θ x
r
X
(5.3)
for all x
X.Replacingx by x in (5.3), we get
f ( 2x) + 2f (x)
Y
1+2
r
θ x
r
X
(5.4)
for all x
X.Letg (x) := ( f (x) ... that
f (x) f ( x)
2
h (x)
Y
2
r
θ
8
r
2
x
3r
X
(4.9)
for all x
X.
Proof. Letting y
= x and z = 2x in (4.8), we get
2 f (x) +...
Báo cáo hóa học: " Research Article Cellular Neural Networks for NP-Hard Optimization" potx
... energy
function, one gets
dE
dt
=−
i,j;k,l
A
i,j;k,l
dy
i,j
dx
i,j
dx
i,j
dt
y
k,l
+ y
i,j
dy
k,l
dx
k,l
dx
k,l
dt
−
b
i,j
dy
i,j
dx
i,j
dx
i,j
dt
u
i,j
=−
i,j
k,l
dy
i,j
dx
i,j
dx
i,j
dt
A
i,j;k,l
y
k,l
−b
i,j
dy
i,j
dx
i,j
dx
i,j
dt
u
i,j
=−
i,j
k,l
dy
i,j
dx
i,j
dx
i,j
dt
A
i,j;k,l
y
k,l
+ ... speed of simulated annealing
(SA) performed on a 3.4 GHz Pentium 4 (squares...
Báo cáo hóa học: " Research Article System of Generalized Implicit Vector Quasivariational Inequalities" potx
... W
i
.Then ,x
i
= f
i
(x) ∈ Co(P
i
(x) ) which contradicts x
i
∈ Co(P
i
(x) ) for all
x
= (x
i
,x
i
) ∈ X.
Thus,
x
i
∈S
i
(x) andG
i
(x) =∅ for each i∈I. That is, x
i
∈S
i
(x) andS
i
(x) ∩ Co(P
i
(x) )=
∅
for ... f
i
(x) ∈ S
i
(x) ifx ∈ W
i
,weknowthatH
i
(x) ⊂ V
i
and so
x ∈ W
i
: f
i
(x) ∈ V
i
∪
x ∈ X : S
i
(x) ⊂ V
i
⊂
x ∈ X : H
i
(x) ⊂ V...
Báo cáo hóa học: " Research Article Rain-Induced Bistatic Scattering at 60 GHz" potx
... interesting results.
5.1. Influence of frequency
For the same link geometry as that of Figure 1, the frequency
dependence from 58 GHz to 66 GHz was investigated. From
Figure 2 it can be seen that the ... study was performed by QinetiQ on behalf of
Ofcom (the UK Office of Communications) to investigate
bistatic scattering at 60 GHz. This study performed a num-
ber of measurements and drafted guid...
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