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1.
Newab Hussain Giuseppe Marino Luigi Muglia Afrah A. N. Abdou 《Journal of Fixed Point Theory and Applications》2016,18(1):1-25
Let H be a Hilbert space, \({(W_n)_{n \in \mathbb{N}}}\) a suitable family of mappings, S a nonexpansive mapping and D a strongly monotone operator. We are interested in the strong convergence of the general schemein dependence of the coefficients \({(\alpha_{n})_{n \in \mathbb{N}}}\) and \({(\mu_{n})_{n \in \mathbb{N}}}\) .
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$$x_{n + 1} = \gamma x_{n} + (1 - \gamma)W_{n} (\alpha_{n}S_{x_{n}} + (1 - \alpha_{n})(I - \mu_{n}D)x_{n}),\quad \gamma \in [0, 1),$$
2.
This work is concerned with an abstract problem in the form of a variational inequality, or equivalently a minimization problem involving a non-differential functional. The problem is inspired by a formulation of the initial–boundary value problem of elastoplasticity. The objective of this work is to revisit the predictor–corrector algorithms that are commonly used in computational applications, and to establish conditions under which these are convergent or, at least, under which they lead to decreasing sequences of the functional for the problem. The focus is on the predictor step, given that the corrector step by definition leads to a decrease in the functional. The predictor step may be formulated as a minimization problem. Attention is given to the tangent predictor, a line search approach, the method of steepest descent, and a Newton-like method. These are all shown to lead to decreasing sequences. 相似文献
3.
A three critical points theorem for nondifferentiable functions is pointed out and an existence result of multiple solutions for a Neumann elliptic variational–hemivariational inequality involving the p-laplacian is established. As an application, a Neumann problem for elliptic equations with discontinuous nonlinearities is studied. 相似文献
4.
We propose a variant of Korpelevich’s method for solving variational inequality problems with operators in Banach spaces.
A full convergence analysis of the method is presented under reasonable assumptions on the problem data. 相似文献
5.
In this paper, well-posedness of a general class of elliptic mixed hemivariational–variational inequalities is studied. This general class includes several classes of the previously studied elliptic mixed hemivariational–variational inequalities as special cases. Moreover, our approach of the well-posedness analysis is easily accessible, unlike those in the published papers on elliptic mixed hemivariational–variational inequalities so far. First, prior theoretical results are recalled for a class of elliptic mixed hemivariational–variational inequalities featured by the presence of a potential operator. Then the well-posedness results are extended through a Banach fixed-point argument to the same class of inequalities without the potential operator assumption. The well-posedness results are further extended to a more general class of elliptic mixed hemivariational–variational inequalities through another application of the Banach fixed-point argument. The theoretical results are illustrated in the study of a contact problem. For comparison, the contact problem is studied both as an elliptic mixed hemivariational–variational inequality and as an elliptic variational–hemivariational inequality. 相似文献
6.
Sokol Bush Kaliaj 《Monatshefte für Mathematik》2014,175(4):555-564
A Banach–Zarecki Theorem for a Banach space-valued function \(F : [0,1] \rightarrow X\) with compact range is presented. We define the strong absolute continuity ( \(sAC_{||.||_{F}}\) ) and the bounded variation ( \(BV_{||.||_{F}}\) ) of \(F\) with respect to the Minkowski functional \(||.||_{F}\) associated to the closed absolutely convex hull \(C_{F}\) of \(F([0,1])\) . It is proved that \(F\) is \(sAC_{||.||_{F}}\) if and only if \(F\) is \(BV_{||.||_{F}}\) , weak continuous on \([0,1]\) and satisfies the weak property \((N)\) . 相似文献
7.
《Operations Research Letters》2021,49(2):283-289
In this paper, we first recall a class of parametric variational–hemivariational inequalities (PVHIs) introduced in Jiang et al. (2020). Then, based on the properties of the Clarke generalized gradient, we establish the Hölder continuity of the solution mapping for PVHIs in terms of regularized gap functions under some assumptions imposed on the data of PVHIs. Finally, an example is given to illustrate our main results. 相似文献
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9.
In this paper, we introduce and study a new system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems and its related auxiliary problems in reflexive Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems. Firstly, we prove the existence and uniqueness of solutions of the auxiliary problems for the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems. Secondly, an iterative algorithm for solving the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems is constructed by using this existence and uniqueness result. Finally, we show the existence of solutions of the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems and discuss the convergence analysis of this algorithm. These results improve, unify and generalize many corresponding known results given in literatures. 相似文献
10.
Hermite–Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert spaces
S.S. Dragomir 《Linear algebra and its applications》2012,436(5):1503-1515
Some Hermite–Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications in relation with the celebrated Hölder–McCarthy’s inequality for positive operators and Ky Fan’s inequality for real numbers are given as well. 相似文献
11.
We present a Kantorovich-type semilocal convergence analysis of the Newton–Josephy method for solving a certain class of variational inequalities. By using a combination of Lipschitz and center-Lipschitz conditions, and our new idea of recurrent functions, we provide an analysis with the following advantages over the earlier works (Wang 2009, Wang and Shen, Appl Math Mech 25:1291–1297, 2004) (under the same or less computational cost): weaker sufficient convergence conditions, larger convergence domain, finer error bounds on the distances involved, and an at least as precise information on the location of the solution. 相似文献
12.
Narin Petrot 《Journal of Applied Mathematics and Computing》2010,32(2):393-404
The purpose of this paper is to suggest and analyze a number of iterative algorithms for solving the generalized set-valued variational inequalities in the sense of Noor in Hilbert spaces. Moreover, we show some relationships between the generalized set-valued variational inequality problem in the sense of Noor and the generalized set-valued Wiener-Hopf equations involving continuous operator. Consequently, by using the equivalence, we also establish some methods for finding the solutions of generalized set-valued Wiener-Hopf equations involving continuous operator. Our results can be viewed as a refinement and improvement of the previously known results for variational inequality theory. 相似文献
13.
We introduce variational inequalities defined in non-pivot Hilbert spaces and we show some existence results. Then, we prove
regularity results for weighted variational inequalities in non-pivot Hilbert space. These results have been applied to the
weighted traffic equilibrium problem. The continuity of the traffic equilibrium solution allows us to present a numerical
method to solve the weighted variational inequality that expresses the problem. In particular, we extend the Solodov-Svaiter
algorithm to the variational inequalities defined in finite-dimensional non-pivot Hilbert spaces. Then, by means of a interpolation,
we construct the solution of the weighted variational inequality defined in a infinite-dimensional space. Moreover, we present
a convergence analysis of the method. 相似文献
14.
Marilyn Breen 《Archiv der Mathematik》1997,68(1):60-64
Let S be a nonempty closed, simply connected set in the plane, and let α τ; 0. If every three points of 5 see a common point of
S via paths of length at most α, then for some point s0 of S, s0 sees each point of S via such a path. That is, S is starshaped via paths of length at most α.
Supported in part by NSF grant DMS-9207019 相似文献
15.
We show the interpolation inequalities for derivatives in variable exponent Lebesgue–Sobolev spaces by applying the boundedness of the Hardy–Littlewood maximal operator on Lp(⋅). 相似文献
16.
This paper is devoted to the study of a class of hemivariational inequalities for the time-dependent Navier–Stokes equations, including both boundary hemivariational inequalities and domain hemivariational inequalities. The hemivariational inequalities are analyzed in the framework of an abstract hemivariational inequality. Solution existence for the abstract hemivariational inequality is explored through a limiting procedure for a temporally semi-discrete scheme based on the backward Euler difference of the time derivative, known as the Rothe method. It is shown that solutions of the Rothe scheme exist, they contain a weakly convergent subsequence as the time step-size approaches zero, and any weak limit of the solution sequence is a solution of the abstract hemivariational inequality. It is further shown that under certain conditions, a solution of the abstract hemivariational inequality is unique and the solution of the abstract hemivariational inequality depends continuously on the problem data. The results on the abstract hemivariational inequality are applied to hemivariational inequalities associated with the time-dependent Navier–Stokes equations. 相似文献
17.
In this paper, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent to a mixed hemivariational–variational inequality. While the minimax principle is of independent interest, it is employed in this paper to provide an elementary proof of the solution existence of the mixed hemivariational–variational inequality. Theoretical results are illustrated in the applications of two contact problems. 相似文献
18.
G. A. Akishev 《Russian Mathematics (Iz VUZ)》2009,53(2):21-29
In this paper we estimate the order of approximation of S. M. Nikol’skii and O. V. Besov classes in the norm of the anisotropic Lorentz space. We also obtain bounds for ortho-diameters of these classes. 相似文献
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20.
Marilyn Breen 《Aequationes Mathematicae》2010,79(1-2):99-110
Let S be a simply connected orthogonal polygon in the plane, and let n be fixed, n ≥ 1. If every two points of S are visible via staircase n-paths from a common point of S, then S is starshaped via staircase (n + 1)-paths. Moreover, the associated staircase (n + 1)-kernel is staircase (n + 1)-convex. The number two is best possible, and the number n + 1 is best possible for n ≥ 2. 相似文献