We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi 1995, 1996 for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is ...

In this paper we introduce a derivative-free, iterative method for solving nonlinear illposed problems Fx = y, where instead of y noisy data yδ with ‖y − yδ‖ ≤ δ are given and F : D(F ) ⊆ X → Y is a nonlinear operator between Hilbert spaces X and Y . This method is defined by splitting the operator F into a linear part A and a nonlinear part G, such that F = A + G. Then iterations are organized...

The aim of this paper is to investigate the global dynamics of a delayed diffusive twostrain disease model. We first study the well-posedness of the model. And then, by selecting appropriate Lyapunov functionals, we demonstrate that the global stability of the model is fully determined by the basic reproduction number. Furthermore, using Schauder fixed point theorem and constructing a pair of u...

This paper presents an algorithm for learning the time-varying shape of a non-rigid 3D object from uncalibrated 2D tracking data. We model shape motion as a rigid component (rotation and translation) combined with a non-rigid deformation. Reconstruction is ill-posed if arbitrary deformations are allowed. We constrain the problem by assuming that the object shape at each time instant is drawn fr...

Ill-posed problems are numerically underdetermined. It is therefore often beneficial to impose known properties of the desired solution, such as nonnegativity, during the solution process. This paper proposes the use of an interior-point method in conjunction with truncated iteration for the solution of large-scale linear discrete ill-posed problems with box constraints. An estimate of the erro...

In a bivariate context, we consider ill-posed inverse problems with incomplete theoretical and data information. We demonstrate the use of information theoretic methods for information recovery for a range of under-identified choice problems with more unknowns than data points. © 2007 Elsevier B.V. All rights reserved.

in this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional cauchy problem with an integral initial condition in banach spaces.

In this paper, we introduce the concept of generalized -contractivityof a pair of maps w.r.t. another pair. We establish a common fixed point result fortwo pairs of self-mappings, when one of these pairs is generalized -contractionw.r.t. the other and study the well-posedness of their fixed point problem. Inparticular, our fixed point result extends the main result of a recent paper ofQingnian ...

In this paper we are interested in a new type of mean-field-type, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths of the state, but also on the conditional law of the state, given the observation to date. Our problem is strongly motivated by the recent study of the mean f...

We report on a new iterative method for regularizing a nonlinear operator equation in Hilbert spaces. The proposed algorithm is a combination of Tikhonov regularization and a fixed point algorithm for the minimization of the Tikhonov–functional. Under the assumptions that the operator F is twice continuous Fréchet–differentiable with Lipschitz– continuous first derivative and that the solution ...