{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:24:34Z","timestamp":1746804274328,"version":"3.40.5"},"reference-count":32,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We prove the demiclosedness principle for a class of mappings which is a generalization of all the forms of nonexpansive, asymptotically nonexpansive, and nearly asymptotically nonexpansive mappings. Moreover, we establish the existence theorem and convergence theorems for modified Ishikawa iterative process in the framework of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>C<\/mml:mi><mml:mi>A<\/mml:mi><mml:mi>T<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>0<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>spaces. Our results generalize, extend, and unify the corresponding results on the topic in the literature.<\/jats:p>","DOI":"10.1155\/2014\/738150","type":"journal-article","created":{"date-parts":[[2014,2,26]],"date-time":"2014-02-26T06:12:41Z","timestamp":1393395161000},"page":"1-10","source":"Crossref","is-referenced-by-count":7,"title":["Demiclosedness Principle for Total Asymptotically Nonexpansive Mappings in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>C<\/mml:mi><mml:mi>A<\/mml:mi><mml:mi>T<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>0<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>Spaces"],"prefix":"10.1155","volume":"2014","author":[{"given":"Erdal","family":"Karap\u0131nar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Atilim University, \u0130ncek 06836, Ankara, Turkey"},{"name":"Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hero","family":"Salahifard","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. 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