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1.
In this paper, we introduce an iterative method for finding a common element of the set of fixed points of a nonexpansive
mapping and the set of common fixed points of a countable family of nonexpansive mappings in Hilbert spaces. Using the result
we consider a strong convergence theorem in variational inequalities and equilibrium problems. The result present in this
paper extend and improve the corresponding result of Qin et al. (Nonlinear Anal 69:3897–3909, 2008), Plubtieng and Punpaeng
(J Math Anal Appl 336:455–469, 2007) and many others. 相似文献
2.
Ying Liu 《Journal of Global Optimization》2010,46(3):319-329
In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively
weak nonexpansive mapping and the set of solutions of a variational inequality in a Banach space. Our results extend and improve
the recent ones announced by Li (J Math Anal Appl 295:115–126, 2004), Jianghua (J Math Anal Appl 337:1041–1047, 2008), and
many others. 相似文献
3.
We consider a generalized equilibrium problem involving DC functions which is called (GEP). For this problem we establish
two new dual formulations based on Toland-Fenchel-Lagrange duality for DC programming problems. The first one allows us to
obtain a unified dual analysis for many interesting problems. So, this dual coincides with the dual problem proposed by Martinez-Legaz
and Sosa (J Glob Optim 25:311–319, 2006) for equilibrium problems in the sense of Blum and Oettli. Furthermore it is equivalent
to Mosco’s dual problem (Mosco in J Math Anal Appl 40:202–206, 1972) when applied to a variational inequality problem. The
second dual problem generalizes to our problem another dual scheme that has been recently introduced by Jacinto and Scheimberg
(Optimization 57:795–805, 2008) for convex equilibrium problems. Through these schemes, as by products, we obtain new optimality
conditions for (GEP) and also, gap functions for (GEP), which cover the ones in Antangerel et al. (J Oper Res 24:353–371,
2007, Pac J Optim 2:667–678, 2006) for variational inequalities and standard convex equilibrium problems. These results, in
turn, when applied to DC and convex optimization problems with convex constraints (considered as special cases of (GEP)) lead
to Toland-Fenchel-Lagrange duality for DC problems in Dinh et al. (Optimization 1–20, 2008, J Convex Anal 15:235–262, 2008),
Fenchel-Lagrange and Lagrange dualities for convex problems as in Antangerel et al. (Pac J Optim 2:667–678, 2006), Bot and
Wanka (Nonlinear Anal to appear), Jeyakumar et al. (Applied Mathematics research report AMR04/8, 2004). Besides, as consequences
of the main results, we obtain some new optimality conditions for DC and convex problems. 相似文献
4.
Hyunseok Kim 《Annali dell'Universita di Ferrara》2009,55(2):279-287
We study the stationary Navier–Stokes equations in a bounded domain Ω of R
3 with smooth connected boundary. The notion of very weak solutions has been introduced by Marušić-Paloka (Appl. Math. Optim.
41:365–375, 2000), Galdi et al. (Math. Ann. 331:41–74, 2005) and Kim (Arch. Ration. Mech. Anal. 193:117–152, 2009) to obtain
solvability results for the Navier–Stokes equations with very irregular data. In this article, we prove a complete solvability
result which unifies those in Marušić-Paloka (Appl. Math. Optim. 41:365–375, 2000), Galdi et al. (Math. Ann. 331:41–74, 2005)
and Kim (Arch. Ration. Mech. Anal. 193:117–152, 2009) by adapting the arguments in Choe and Kim (Preprint) and Kim and Kozono
(Preprint). 相似文献
5.
In this paper, we introduce two iterative schemes (one implicit and one explicit) for finding a common element of the set
of solutions of the generalized equilibrium problems and the set of all common fixed points of a nonexpansive semigroup in
the framework of a real Hilbert space. We prove that both approaches converge strongly to a common element of such two sets.
Such common element is the unique solution of a variational inequality, which is the optimality condition for a minimization
problem. Furthermore, we utilize the main results to obtain two mean ergodic theorems for nonexpansive mappings in a Hilbert
space. The results of this paper extend and improve the results of Li et al. (J Nonlinear Anal 70:3065–3071, 2009), Cianciaruso et al. (J Optim Theory Appl 146:491–509, 2010) and many others. 相似文献
6.
The purpose of this paper is to consider a shrinking projection method of finding the common element of the set of common
fixed points for a finite family of a ξ-strict pseudo-contraction, the set of solutions of a systems of equilibrium problems
and the set of solutions of variational inclusions. Then, we prove strong convergence theorems of the iterative sequence generated
by the shrinking projection method under some suitable conditions in a real Hilbert space. Our results improve and extend
recent results announced by Peng, Wang, Shyu and Yao (J Inequal Appl, 2008:15, Article ID 720371, 2008), Takahashi, Takeuchi and Kubota (J Math Anal Appl 341:276–286, 2008), Takahashi and Takahashi (Nonlinear Anal 69:1025–1033, 2008) and many others. 相似文献
7.
In this paper, we focus on the restoration of images that have incomplete data in either the image domain or the transformed
domain or in both. The transform used can be any orthonormal or tight frame transforms such as orthonormal wavelets, tight
framelets, the discrete Fourier transform, the Gabor transform, the discrete cosine transform, and the discrete local cosine
transform. We propose an iterative algorithm that can restore the incomplete data in both domains simultaneously. We prove
the convergence of the algorithm and derive the optimal properties of its limit. The algorithm generalizes, unifies, and simplifies
the inpainting algorithm in image domains given in Cai et al. (Appl Comput Harmon Anal 24:131–149, 2008) and the inpainting
algorithms in the transformed domains given in Cai et al. (SIAM J Sci Comput 30(3):1205–1227, 2008), Chan et al. (SIAM J Sci
Comput 24:1408–1432, 2003; Appl Comput Harmon Anal 17:91–115, 2004). Finally, applications of the new algorithm to super-resolution
image reconstruction with different zooms are presented.
R. H. Chan’s research was supported in part by HKRGC Grant 400505 and CUHK DAG 2060257.
L. Shen’s research was supported by the US National Science Foundation under grant DMS-0712827.
Z. Shen’s research was supported in part by Grant R-146-000-060-112 at the National University of Singapore. 相似文献
8.
Frédéric Bernicot 《Journal of Geometric Analysis》2010,20(1):39-62
In this paper we construct a new class of bilinear pseudodifferential operators which contains both the Coifman-Meyer class
as well as the non-translation invariant class closely related both to the bilinear Hilbert transform and previously studied
in Bényi et al. (J. Geom. Anal. 16(3):431–453, 2006), Bényi et al. (J. Anal. Math., 2009), Bernicot (Anal. PDE 1:1–27, 2008) as well as the bilinear Marcinkiewicz class studied in Grafakos and Kalton (Stud. Math. 146(2):115–156, 2001). We prove boundedness on Sobolev spaces for these operators as well as establish a symbolic calculus that exhibits the nice
behavior of our new class under transposition and composition with linear operators. 相似文献
9.
In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the solutions of the variational inequality problem for two inverse-strongly monotone mappings. We introduce a new viscosity relaxed extragradient approximation method which is based on the so-called relaxed extragradient method and the viscosity approximation method. We show that the sequence converges strongly to a common element of the above three sets under some parametric controlling conditions. Moreover, using the above theorem, we can apply to finding solutions of a general system of variational inequality and a zero of a maximal monotone operator in a real Hilbert space. The results of this paper extended, improved and connected with the results of Ceng et al., [L.-C. Ceng, C.-Y. Wang, J.-C. Yao, Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Meth. Oper. Res. 67 (2008), 375–390], Plubtieng and Punpaeng, [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings, Appl. Math. Comput. 197 (2) (2008) 548–558] Su et al., [Y. Su, et al., An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal. 69 (8) (2008) 2709–2719], Li and Song [Liwei Li, W. Song, A hybrid of the extragradient method and proximal point algorithm for inverse strongly monotone operators and maximal monotone operators in Banach spaces, Nonlinear Anal.: Hybrid Syst. 1 (3) (2007), 398-413] and many others. 相似文献
10.
The purpose of this paper is to prove some new common fixed point theorems in (GV)-fuzzy metric spaces. While proving our results, we utilize the idea of compatibility due to Jungck (Int J Math Math Sci
9:771–779, 1986) together with subsequentially continuity due to Bouhadjera and Godet-Thobie (arXiv: 0906.3159v1 [math.FA] 17 Jun 2009) respectively (also alternately reciprocal continuity due to Pant (Bull Calcutta Math Soc 90:281–286, 1998) together with subcompatibility due to Bouhadjera and Godet-Thobie (arXiv:0906.3159v1 [math.FA] 17 Jun 2009) as patterned in Imdad et al. (doi:) wherein conditions on completeness (or closedness) of the underlying space (or subspaces) together with conditions on continuity
in respect of any one of the involved maps are relaxed. Our results substantially generalize and improve a multitude of relevant
common fixed point theorems of the existing literature in metric as well as fuzzy metric spaces which include some relevant
results due to Imdad et al. (J Appl Math Inform 26:591–603, 2008), Mihet (doi:), Mishra (Tamkang J Math 39(4):309–316, 2008), Singh (Fuzzy Sets Syst 115:471–475, 2000) and several others. 相似文献
11.
In this paper, we introduce and study a new iterative scheme for finding the common element of the set of common fixed points
of a sequence of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the general
system of variational inequality for α and μ-inverse-strongly monotone mappings. We show that the sequence converges strongly to a common element of the above three sets
under some parameters controlling conditions. This main theorem extends a recent result of Ceng et al. (Math Meth Oper Res
67:375–390, 2008) and many others. 相似文献
12.
In this paper, we introduce an iterative scheme based on a viscosity approximation method with a modified extragradient method
for finding a common solutions of a general system of variational inequalities for two inverse-strongly accretive operator
and solutions of fixed point problems involving the nonexpansive mapping in Banach spaces. Consequently, we obtain new strong
convergence theorems in the frame work of Banach spaces. Our results extend and improve the recent results of Qin et al. (J
Comput Appl Math 233:231–240, 2009) and many others. 相似文献
13.
We introduce a new iterative method in order to approximate a locally unique solution of variational inclusions in Banach
spaces. The method uses only divided differences operators of order one. An existence–convergence theorem and a radius of
convergence are given under some conditions on divided difference operator and Lipschitz-like continuity property of set-valued
mappings. Our method extends the recent work related to the resolution of nonlinear equation in Argyros (J Math Anal Appl
332:97–108, 2007) and has the following advantages: faster convergence to the solution than all the previous known ones in Argyros and Hilout
(Appl Math Comput, 2008 in press), Hilout (J Math Anal Appl 339:53–761, 2008, Positivity 10:673–700, 2006), and we do not need to evaluate any Fréchet derivative. We provide also an improvement of the ratio of our algorithm under
some center-conditions and less computational cost. Numerical examples are also provided.
相似文献
14.
In this paper we analyze the hydrodynamic equations for Ginzburg–Landau vortices as derived by E (Phys. Rev. B. 50(3):1126–1135,
1994). In particular, we are interested in the mean field model describing the evolution of two patches of vortices with equal
and opposite degrees. Many results are already available for the case of a single density of vortices with uniform degree.
This model does not take into account the vortex annihilation, hence it can also be seen as a particular instance of the signed
measures system obtained in Ambrosio et al. (Ann. Inst. H. Poincaré Anal. Non Linéaire 28(2):217–246, 2011) and related to the Chapman et al. (Eur. J. Appl. Math. 7(2):97–111, 1996) formulation. We establish global existence of L
p
solutions, exploiting some optimal transport techniques introduced in this context in Ambrosio and Serfaty (Commun. Pure
Appl. Math. LXI(11):1495–1539, 2008). We prove uniqueness for L
∞ solutions, as expected by analogy with the incompressible Euler equations in fluidodynamics. We also consider the corresponding
Dirichlet problem in a bounded domain. Moreover, we show some simple examples of 1-dimensional dynamic. 相似文献
15.
In this paper we describe how techniques of asymptotic analysis can be used in a systematic way to perform ‘aggregation’ of
variables, based on a separation of different time scales, in a population model with age and space structure. The main result
of the paper is proving the convergence of the formal asymptotic expansion to the solution of the original equation. This
result improves and clarifies earlier results of Arino et al. (SIAM J Appl Math 60(2):408–436, 1999), Auger et al. (Structured population models in biology and epidemiology. Springer Verlag, Berlin, 2008), Lisi and Totaro (Math Biosci 196(2):153–186, 2005). 相似文献
16.
Zhaoyin Xiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,50(4):467-478
In this paper, we deal with the global existence and nonexistence of solutions to a diffusive polytropic filtration system
with nonlinear boundary conditions. By constructing various kinds of sub- and super-solutions and using the basic properties
of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions, which extend the
recent results of Li et al. (Z Angew Math Phys 60:284–298, 2009) and Wang et al. (Nonlinear Anal 71:2134–2140, 2009) to more
general equations and simplify their proofs slightly. 相似文献
17.
Recently, O’Hara, Pillay and Xu (Nonlinear Anal. 54, 1417–1426, 2003) considered an iterative approach to finding a nearest common fixed point of infinitely many nonexpansive mappings in a Hilbert
space. Very recently, Takahashi and Takahashi (J. Math. Anal. Appl. 331, 506–515, 2007) introduced an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions
of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. In this paper, motivated
by these authors’ iterative schemes, we introduce a new iterative approach to finding a common element of the set of solutions
of an equilibrium problem and the set of common fixed points of infinitely many nonexpansive mappings in a Hilbert space.
The main result of this work is a strong convergence theorem which improves and extends results from the above mentioned papers. 相似文献
18.
Kiyoshi Takeuchi 《Mathematische Annalen》2010,348(4):815-831
We study non-confluent A-hypergeometric systems introduced by Gelfand et al. (Funct Anal Appl 23:94–106, 1989) and prove a formula for the eigenvalues
of their monodromy automorphisms defined by the analytic continuations along large loops contained in complex lines parallel
to the coordinate axes. The method of toric compactifications introduced in Libgober and Sperber (Compositio Math 95:287–307,
1995) and Matsui and Takeuchi (Mathematische Zeitschrift) will be used to prove our main theorem. 相似文献
19.
Jong Soo Jung 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):449-459
In this paper, we introduce a composite iterative scheme by viscosity approximation method for finding a zero of an accretive operator in Banach spaces. Then, we establish strong convergence theorems for the composite iterative scheme. The main theorems improve and generalize the recent corresponding results of Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51-60], Qin and Su [X. Qin, Y. Su, Approximation of a zero point of accretive operator in Banach spaces, J. Math. Anal. Appl. 329 (2007) 415-424] and Xu [H.K. Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631-643] as well as Aoyama et al. [K. Aoyama, Y Kimura, W. Takahashi, M. Toyoda, Approximation of common fixed points of a countable family of nonexpansive mappings in Banach spaces, Nonlinear Anal. 67 (2007) 2350-2360], Benavides et al. [T.D. Benavides, G.L. Acedo, H.K. Xu, Iterative solutions for zeros of accretive operators, Math. Nachr. 248-249 (2003) 62-71], Chen and Zhu [R. Chen, Z. Zhu, Viscosity approximation fixed points for nonexpansive and m-accretive operators, Fixed Point Theory and Appl. 2006 (2006) 1-10] and Kamimura and Takahashi [S. Kamimura, W. Takahashi, Approximation solutions of maximal monotone operators in Hilberts spaces, J. Approx. Theory 106 (2000) 226-240]. 相似文献
20.
In this paper, we study a two-phase liquid–gas model with constant viscosity coefficient when both the initial liquid and
gas masses connect to vacuum continuously. Just as in Evje and Karlsen (Commun Pure Appl Anal 8:1867–1894, 2009) and Evje
et al. (Nonlinear Anal 70:3864–3886, 2009), the gas is assumed to be polytropic whereas the liquid is treated as an incompressible
fluid. We use a new technique to get the upper and lower bounds of gas and liquid masses n and m. Then we get the global existence of weak solution by the line method. Also, we obtain the uniqueness of the weak solution. 相似文献