Original scientific paper
https://doi.org/10.17535/crorr.2022.0009
A Valuable Remark on Lipschitz in the First Variable Definition and System of Nonlinear Variational Inequalities
Ayache Benhadid
orcid.org/0000-0001-7567-2192
; Department of Mathematics, Faculty of Mathematics and Computer Science
Abstract
The goal of this paper is to present a critique on the incorrect use of the Lipschitz definition concerning the first variable and/or the second variable in the literature on the system of variational inequalities by many authors. The possible impact of this paper is rather important, it questions the results of different authors, particularly when taking into account that some of these papers are published in quite good mathematical journals. As a result, not only that the proofs are wrong, but also the credibility of the theorems themselves is compromised. In addition, this paper illustrate, using a counterexample, that there is an error in setting up first variable definition and the results obtained in listed references do not hold up in H × H.
Keywords
Lipschitz continuous mappings; System of variational inequalities with different nonlinear mappings
Hrčak ID:
280268
URI
Publication date:
12.7.2022.
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