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online May 19th, 2014 by T. Haddad and T. Haddad entitled "Delay perturbed statedependent sweeping process" .
First, The authors are in breach of the rules of submission for applicable Analysis,
and of the warranty made to Taylor & Francis regarding originality since the authors
failed to cite, reference or acknowledge their previous work published in Journal of
Nonlinear Science and Applications, available online atwww.tjnsa.com, J.
Nonlin.Sci. Appl. 7 (2014), 70-77, ISSN 2008-1901 " Existence of solutions to the
state dependent sweeping process with delay" ( received 2012 -11- 23, I have
attached a copy of the paper).
Only for this reason, the paper must be removed, the two papers deal with the same
problem with the same assumptions, the same method, the same result, the only
difference is the assumption on the set C (t, u (t) ) which is convex in the first and
uniformly r-prox regular in the second, which is a form of local convexity, and all the
experts know that it is enough to choose a finer discretization ie. choose n large
enough to recover the convexity and the proof is exactly the same. (Notice that the
referees of your journal made some important corrections with regard to the first
one).
In fact, there is an obvious likeness between both papers and a result ( theorem 3.5) in
my joint paper with C. Castaing and G. Ibrahim entitled " Some contributions to
nonconvex sweeping process " published in Journal of Nonlinear and Convex
Analysis, Vol. 10, N 1, 2009, 1-20 (see attached file). I leave it to you to check that
there is no scientific contribution and it is the same problem with the same
assumptions, the same method, the same result and the same steps. The only
difference is not fundamental or major and makes no changes to the proof, it concerns
the estimation of the elements of the sequence (equation 4 in the paper), they obtain
our same constant in a classic way while the novelty (and the strength) of our result
lies in the use of the fixed point because our assumptions (C3) depends on t, u and x.
Notice that their algorithm is not new since it was already used by other authors, of
whom Kaadour Chraibi in his Ph D thesis,1987, Montpellier, see the reference :
Kunze M. and Monteiro Marques M.D.P. "On parabolic quasi variational inequalities
and state dependent sweeping process" in Topological Methods in Nonlinear
Analysis, Vol. 12, 1998, 179-191, page 181, line 13.
Notice also that in our paper, we deal with uniformly r-prox regular sets C(t,u(t)); and
as in the case of the second order problem (theorems 3.2 and 3.3), we give the result
with r-prox regularity condition for the problem without perturbation (Theorem 3.4)
and for simplicity we do with convex C for the perturbed problem (theorem 3.5) since
we know how to go to the r-prox regular case.
I understand that the referees cannot know because our paper of JNCA is not
available online, but in my opinion, there is no major scientific contribution in both
papers, I leave you the care of making the necessary decisions.
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