{"id":17970,"date":"2023-10-13T13:10:25","date_gmt":"2023-10-13T05:10:25","guid":{"rendered":"https:\/\/cantor.math.ntnu.edu.tw\/?p=17970"},"modified":"2023-10-13T13:11:42","modified_gmt":"2023-10-13T05:11:42","slug":"talk20231215","status":"publish","type":"post","link":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/2023\/10\/13\/talk20231215\/","title":{"rendered":"<span style=\"color:#3566BD\">[\u5c08\u984c\u6f14\u8b1b] <\/span>\u301012\u670815\u65e5\u3011Adrian Petrusel \/ MULTI-VALUED CONTRACTION PRINCIPLE (THEORY AND APPLICATIONS) AFTER (MORE THAN) HALF CENTURY"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"17970\" class=\"elementor elementor-17970\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5c5458f6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5c5458f6\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-43b8ceff\" data-id=\"43b8ceff\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4115cdb6 elementor-widget elementor-widget-heading\" data-id=\"4115cdb6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">MULTI-VALUED CONTRACTION PRINCIPLE\n(THEORY AND APPLICATIONS)\nAFTER (MORE THAN) HALF CENTURY<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-699139af elementor-widget elementor-widget-spacer\" data-id=\"699139af\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-619e1f6 elementor-widget elementor-widget-text-editor\" data-id=\"619e1f6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: bold;\">Time: December 15 (Friday, 15:00)\u00a0 \/\u00a0 Place: S506, Gongguan Campus, NTNU<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-11dc7f58 elementor-widget elementor-widget-image\" data-id=\"11dc7f58\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"200\" height=\"239\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2023\/10\/20231215_Adrian.jpg\" class=\"attachment-full size-full wp-image-17971\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-33877fad elementor-widget elementor-widget-text-editor\" data-id=\"33877fad\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 22px; line-height: 26px; text-align: center; color: #cc6633; font-weight: bold;\">Prof. Adrian Petrusel<\/div><div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 18px; line-height: 22px; text-align: center; color: #cc9966; font-weight: bold;\">( Vice Rector of Babe\u015f-Bolyai University, Romania)<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5de4ac7d elementor-widget elementor-widget-spacer\" data-id=\"5de4ac7d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cf4b31e elementor-widget elementor-widget-text-editor\" data-id=\"cf4b31e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In this talk, we will present, in the context of a complete metric space (X, d), several results concerning existence, uniqueness, data dependence, stability properties for the fixed point inclusion x \u2208 F(x), as well as various qualitative properties for the fixed point set of a multi-valued contraction F : X \u2014\u03bf X in the sense of Nadler, see [2], [1]. Applications and extensions to other problems of the metric fixed point theory are suggested.<\/p><p style=\"text-align: left;\"><span style=\"color: #808080;\">References<\/span><\/p><p style=\"text-align: left;\"><span style=\"color: #808080;\">[1] H. Covitz, S.B. Nadler jr., Multivalued contraction mappings in generalized metric <\/span><span style=\"color: #808080;\">spaces, Israel J. Math., 8(1970) 5-11.<\/span><br \/><span style=\"color: #808080;\">[2] S.B. Nadler Jr., Multivalued contraction mappings, Pacific J. Math., 30(1969) 475-<\/span><span style=\"color: #808080;\">488.<\/span><br \/><span style=\"color: #808080;\">[3] A. Petrusel, I.A. Rus, M.A. Serban, Basic problems of the metric fixed point the<\/span><span style=\"color: #808080;\">ory and the relevance of a metric fixed point theorem for multivalued operators, J. <\/span><span style=\"color: #808080;\">Nonlinear Convex Anal., 15(2014), no.3, 493-513.<\/span><br \/><span style=\"color: #808080;\">[4] A. Petrusel, G. Petrusel, J.C. Yao, Multivalued graph contraction principle, Optimiza<\/span><span style=\"color: #808080;\">tion, 69(2020), no. 7-8, 1541-1556.<\/span><br \/><span style=\"color: #808080;\">[5] A. Petrusel, G. Petrusel, Some variants of the contraction principle for multi-valued <\/span><span style=\"color: #808080;\">operators, generalizations and applications, J. Nonlinear Convex Anal. 20 (2019), no.<\/span><br \/><span style=\"color: #808080;\">10, 2187-2203.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d369826 elementor-widget elementor-widget-image\" data-id=\"d369826\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1240\" height=\"758\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e.jpg\" class=\"attachment-full size-full wp-image-7367\" alt=\"\" srcset=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e.jpg 1240w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-300x183.jpg 300w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-768x469.jpg 768w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-1024x626.jpg 1024w\" sizes=\"(max-width: 1240px) 100vw, 1240px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>MULTI-VALUED CONTRACTION PRINCIPLE (THEORY AND APPLICAT 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