... collection of events, sigma-algebra
A
filtration
E(X) expectation of X
E(X |A) conditional expectation of X under A
P (A) probability of A
P (A |B) probability of A conditioned on B
∈ element of
∈ ... context of derivative pricing.
The book does not claim to be a complete account of the state of the
art of the subject. Rather it attempts to provide a systematic framework for
an understanding of ... covering many new results for the approxi-
mation of continuous solutions of SDEs. The discrete time approximation of
SDEs with jumps represents the focus of the monograph. The reader learns
about powerful...
... for solving
different classes ofsystemsof nonlinear matrix equations involving Lipshitzian
mappings.
2000 Mathematics Subject Classifications: 15A24; 65H05.
Keywords: nonlinear matrix equations, ... 2011:89
http://www.fixedpointtheoryandapplications.com/content/2011/1/89
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RESEARC H Open Access
Solving systemsof nonlinear matrix equations
involving Lipshitzian mappings
Maher Berzig
*
and Bessem ... for the
study of solutions to systemsof nonlinear matrix equations involving contractive
mappings.
We first review the Thompson metric on the open convex cone P(n)(n ≥ 2), the set
of all nìn Hermitian...
... asymptotic stability of the non-
linear impulsive stochastic differentialequations and the impulsive stochastic partial
differential equationswith infinite delays by means of the fixed point ... stochastic partial
differential equationswith delays by the fixed point method. Zhou and Zhong [15]
study the exponential p-stability of neutral stochastic differentialequationswith multi-
ple ... neutral differentialequationswith variable delays. Proc Am Math Soc. 136,
909–918 (2008)
19. Ardjouni, A, Djoudi, A: Fixed points and stability in linear neutral differentialequationswith variable...
... integro -differential equations with
deviating arguments. J Comput Appl Math 2009, 225:602-611.
45. Wang G: Boundary value problems for systemsof nonlinear integro -differential equationswith deviating
arguments. ... nonlinear ordinary differentialequationswith advanced
arguments. Nonlinear Anal 2003, 53:495-505.
40. Yan JR: Oscillation of first-order impulsive differentialequationswith advanced argument. ... fractional integrodifferential equations in
Banach spaces. Nonlinear Anal 2010, 72:4587-4593.
28. Goodrich ChS: Existence of a positive solution to a class of fractional differential equations. Appl...
... The proof of uniqueness is complete.
To prove the existence we note, first of all, that it suffices to provide a
proof if one of the κ
i
’s is equal to ±1 and one of the δ
j
’s is equal to ∓1 with
all ... solution of the difference Schlesinger equations (3.1)–
(3.3) with the initial conditions {B
i
(0) = B
i
}, and let B
i
(x
1
, ,x
n
)bethe
solution of the classical Schlesinger equations (5.4) with ... solutions of
isomonodromy problems for such systemsof difference equations. In the case
of one-interval gap probability this has been done (in a different language) in
[Bor], [BB]. One example of the...
... the development of general solutions to systemsof linear differential
equations or higher order linear differential equations.
Over the past decade or two, first-order differentialequations have ... will encounter a handful of examples on linear
differential equations that foreshadow part of the role of linear algebra in the
field ofdifferential equations. The goal of the chapter on linear ... for the solution of linear systems of
differentialequations in chapter 3. Discussion of ideas like basis, dimension,
and vector spaces of functions from the final two sections of chapter 1 can...
... lower and upper solutions for problem (1) with Λ = 0, and this does not
depend on the choice of τ.
Proof. Reasoning in the same way as in the proof of Proposition 1, we
obtain that there exists ... the
recent articles [2–7] which deal with existence results for this kind of prob-
lems. For the qualitative study of this type of problems we can cite the
survey of Hartung et al. [8] and references ... differential
equations with deviated arguments. J. Optim. Theory Appl. 135(2), 257–269
(2007)
5. Jankowski, T: Existence of solutions of boundary value problems for dif-
ferential equations in...