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Under some natural assumptions we prove that the sequence generated by the algorithm is convergent for the pseudomonotone case and assuming an extra condition on the solution set we prove the convergence for the quasimonotone case. This approach unifies the results obtained by Auslender <jats:italic>et al.<\/jats:italic> [<jats:italic>Math Oper. Res.<\/jats:italic> <jats:bold>24<\/jats:bold> (1999) 644\u2013688] and Brito <jats:italic>et al.<\/jats:italic> [<jats:italic>J. Optim. Theory Appl.<\/jats:italic> <jats:bold>154<\/jats:bold> (2012) 217\u2013234] and extends the convergence properties for the class of <jats:italic>\u03c6<\/jats:italic>-divergence distances and Bregman distances.<\/jats:p>","DOI":"10.1051\/ro\/2017078","type":"journal-article","created":{"date-parts":[[2017,10,17]],"date-time":"2017-10-17T06:37:56Z","timestamp":1508222276000},"page":"159-176","source":"Crossref","is-referenced-by-count":8,"title":["An inexact algorithm with proximal distances for variational inequalities"],"prefix":"10.1051","volume":"52","author":[{"given":"E.A.","family":"Papa Quiroz","sequence":"first","affiliation":[]},{"given":"L.","family":"Mallma Ramirez","sequence":"additional","affiliation":[]},{"given":"P.R.","family":"Oliveira","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2018,4,23]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Ansari Q.H., \nLalitha C.S. and \nMehta M., \nGeneralized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization. \nTaylor Francis Group \n(2014) 122.","DOI":"10.1201\/b15244"},{"key":"R2","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1137\/S1052623403427823","volume":"16","author":"Auslender","year":"2006","journal-title":"SIAM J. 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