Báo cáo hóa học: " Research Article Application of the Subordination Principle to the Harmonic Mappings Convex in One Direction with Shear Construction Method" pot
... |wz| < 1.
In this paper we examine the class of functions that are convex in one direction.
The shear construction is essential to the present work as it allows one to study harmonic
functions ... Subordination Principle to
the Harmonic Mappings Convex in One Direction
with Shear Construction Method
Yas¸ar Polato
˘
glu, H. Esra
¨
Ozk...
... split into a fixed number of bands [14]. So, in
respect to calculation of coefficients, given in (3)and(4), the
following working parameters are to be determined, namely,
the initial number of time-variant ... physical
interpretation of selected set of features.
Nonetheless, and just for the sake of illustration, this
work carries out tuning of proposed training appro...
... and nontrivial
estimates in the proof.
2. Proof of Theorem 1.2
Let us begin with recalling some known conclusion.
Similar to the proof of 17, we can easily get the following.
Lemma 2.1. If Ω satisfies ... Journal of Inequalities and Applications
15 E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series,
no. 30, Prince...
... and using the similar proof of
Theorem 3.1, we can obtain the result easily.
4. A Numerical Example
In the following, we give an example to illustrate the validity of our method.
4 Advances in Difference ... the conditions in the theorem are dependent on the
upper bound of the derivative of time-varying delay and the delay kernels h
j
,j ∈
Λ, and independent...
... the relation w
≡ 0 from this inequality with the use of Gronwall
inequality. Then, v ≤ u in
D
T
, and the proof of part i of the lemma is completed. The similar
argument gives the proof of ... possess the properties 2.30 and 2.31 for the case m 1. By the
principle of induction, we complete the proof of the lemma.
3. Uniform Estimates of {u
m...
... 0 then the
point x
n−k
,y
n−k
is on the line containing the fixed point which is parallel to L.
Remark 4.6. Notice that, according to the results in 8, when |λ| ρ and the argument θ of
the ... α
2
.
Proof. As we have seen in Section 2, the solution to System 1.2 starting at a point x
0
,y
0
not
belonging to the forbidden set is just the projection by...
... with delays. Therefore, in this paper, we consider a boundary
value problem of a general delayed nonlinear fractional system. With the help of some fixed point
theorems and the properties of the ... Therefore, the
obtained results generalize and include some existing ones.
The remaining part of this paper is organized as follows. In Section 2,weintroduce
some basics...
... description of the dynamics. One of the possible gener-
alizations of Langevin equation is to replace the ordinary derivative by a fractional derivative
in it. This gives rise to fractional Langevin equation, ... problem to Langevin equation involving two fractional orders. The
Banach fixed point theorem and Krasnoselskii’s fixed point theorem are applied to establish...
... main results, we also need the following lemmas.
The first part of the next lemma is an immediate consequence of the subdifferential
inequality, and the proof of the second part can be found in ... αα
n
}.Inviewof
Lemma 2.4, we can obtain the desired conclusion easily. This completes the proof.
As an application of Theorems 3.1 and 3.2, we have the following resul...
... α-inverse-
strongly monotone mapping of C into H, and let S be a nonexpansive mapping of C into itself such
that FS ∩ Ω
/
∅,whereΩ denotes the set of solutions of a variational inequality for the α-inverse-
strongly ... the following theorem.
Theorem IT. Let C be a closed convex subset of a real Hilbert space H.LetA be an α-inverse-
strongly monotone mapping of C into...