{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:45:24Z","timestamp":1753886724441,"version":"3.41.2"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,4,7]],"date-time":"2011-04-07T00:00:00Z","timestamp":1302134400000},"content-version":"vor","delay-in-days":96,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>We establish some versions of fixed\u2010point theorem in a Frechet topological vector space <jats:italic>E<\/jats:italic>. The main result is that every map <jats:italic>A<\/jats:italic> = <jats:italic>B<\/jats:italic><jats:italic>C<\/jats:italic> (where <jats:italic>B<\/jats:italic> is a continuous map and <jats:italic>C<\/jats:italic> is a continuous linear weakly compact operator) from a closed convex subset of a Frechet topological vector space having the Dunford\u2010Pettis property into itself has fixed\u2010point. Based on this result, we present two versions of the Krasnoselskii fixed\u2010point theorem. Our first result extend the well\u2010known Krasnoselskii\u2032s fixed\u2010point theorem for <jats:italic>U<\/jats:italic>\u2010contractions and weakly compact mappings, while the second one, by assuming that the family {<jats:italic>T<\/jats:italic>(\u00b7, <jats:italic>y<\/jats:italic>) : <jats:italic>y<\/jats:italic> \u2208 <jats:italic>C<\/jats:italic>(<jats:italic>M<\/jats:italic>) where <jats:italic>M<\/jats:italic> \u2282 <jats:italic>E<\/jats:italic> and <jats:italic>C<\/jats:italic> : <jats:italic>M<\/jats:italic> \u2192 <jats:italic>E<\/jats:italic> a compact operator} is nonlinear <jats:italic>\u03c6<\/jats:italic> equicontractive, we give a fixed\u2010point theorem for the operator of the form <jats:italic>E<\/jats:italic><jats:italic>x<\/jats:italic> :  = <jats:italic>T<\/jats:italic>(<jats:italic>x<\/jats:italic>, <jats:italic>C<\/jats:italic>(<jats:italic>x<\/jats:italic>)).<\/jats:p>","DOI":"10.1155\/2011\/390720","type":"journal-article","created":{"date-parts":[[2011,4,7]],"date-time":"2011-04-07T19:33:58Z","timestamp":1302204838000},"update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fixed\u2010Point Theory on a Frechet Topological Vector Space"],"prefix":"10.1155","volume":"2011","author":[{"given":"Afif","family":"Ben Amar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed Amine","family":"Cherif","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maher","family":"Mnif","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,4,7]]},"reference":[{"key":"e_1_2_4_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0893\u20109659(97)00138\u20109"},{"key":"e_1_2_4_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19981890103"},{"key":"e_1_2_4_3_2","first-page":"49","article-title":"Local fixed point theory for the sum of two operators in Banach spaces","volume":"4","author":"Dhage B. 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