A Valuable Remark on Lipschitz in the First Variable Definition and System of Nonlinear Variational Inequalities
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 variationalinequalities 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.
Downloads
Published
Issue
Section
License
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
