Variational techniques for data assimilation, i.e., estimating orbits of dynamical models from observations, are revisited. It is shown that under mild hypotheses a solution to this variational problem exists. Using ideas from optimal control theory, the problem of uniqueness is investigated and a number of results (well known from optimal control) are established in the present context. The va...

This paper introduces a new fractional variational optical flow model, which combines the fractional derivative with the variational optical flow method, for motion estimation. In the model, the data term is a weighted least-squares fit of local brightness constraint function and the prior term is a fractional derivative penalty function. So the proposed model can be seen as generalizations of ...

Let Cb(K) be the set of all bounded continuous (real or complex) functions on a complete metric space K and A a closed subspace of Cb(K). Using the variational method, it is shown that the set of all strong peak functions in A is dense if and only if the set of all strong peak points is a norming subset of A. As a corollary we show that if X is a locally uniformly convex, complex Banach space, ...

Let E be a real Banach space with a uniformly Gâteaux differentiable norm and which possesses uniform normal structure, K a nonempty bounded closed convex subset of E, {Ti}i=1 a finite family of asymptotically nonexpansive self-mappings on K with common sequence {kn}∞n=1 ⊂ [1,∞), {tn}, {sn} be two sequences in (0, 1) such that sn + tn = 1 (n ≥ 1) and f be a contraction on K . Under suitable con...

Let E be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let J {T t : t ≥ 0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of E, with functions u, v : 0,∞ → 0,∞ . Let F : F J ∩t≥0F T t / ∅ and f : K → K be a weakly contractive map. For some positive real numbers λ and δ satisfying δ λ > 1, let G ...

Prox-regularity of a set (Poliquin-Rockafellar-Thibault, 2000), or its global version, proximal smoothness (Clarke-Stern-Wolenski, 1995) plays an important role in variational analysis, not only because it is associated with some fundamental properties as the local continuous differentiability of the function dist (C; ·), or the local uniqueness of the projection mapping, but also because in th...

An extended variational iteration method within the local fractional derivative is introduced for first time, where two Lagrange multipliers are adopted. Moreover, sufficient conditions convergence of new also established.

We have shown recently that the gravity field phenomena can be described by a traceless part of the wave-type field equation. This is an essentially non-Einsteinian gravity model. It has an exact sphericallysymmetric static solution, that yields to the Yilmaz-Rosen metric. This metric is very close to the Schwarzchild metric. The wave-type field equation can not be derived from a suitable varia...

Let X be a uniformly convex Banach space and S {T s : 0 ≤ s < ∞} be a nonexpansive semigroup such that F S ⋂s>0 F T s / ∅. Consider the iterative method that generates the sequence {xn} by the algorithm xn 1 αnf xn βnxn 1 − αn − βn 1/sn ∫sn 0 T s xnds, n ≥ 0, where {αn}, {βn}, and {sn} are three sequences satisfying certain conditions, f : C → C is a contraction mapping. Strong convergence of t...