{"created":"2021-03-01T05:58:50.175992+00:00","id":6402,"links":{},"metadata":{"_buckets":{"deposit":"c0053438-a0cb-419e-adda-52a7fc5cd2cf"},"_deposit":{"id":"6402","owners":[],"pid":{"revision_id":0,"type":"depid","value":"6402"},"status":"published"},"_oai":{"id":"oai:kitami-it.repo.nii.ac.jp:00006402","sets":["7:15:23"]},"item_2_biblio_info_6":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1976-06","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"443","bibliographicPageStart":"441","bibliographicVolumeNumber":"7","bibliographic_titles":[{"bibliographic_title":"北見工業大学研究報告"}]}]},"item_2_description_14":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_2_description_4":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"Let f（x） be differentiable, α＜x＜β． We putr(x, y) = { (f(x)?f(y))/(x?y), x≠y, f´(x),　         ｘ＝ｙ　　        （1）We have the following :(i)　 r(x, y)＝r(y, x),(ii)  r(x, z)(x?z)＝r(x, y)(x?y)＋r(y, z)(y?z),(iii)　<lim>___x→y r(x, y)＝r(y, y),(iv)　r is continuous at a point (x, y) of x≠y. Newly, having no relation to (1), let r(x, y) be a real function of 2-varia-bles, α＜x, y＜β. In ［1］, if r(x, y) satisfies the previous (i), (ii), (iii), (iv), then we obtain Rolle’s theorem and mean value theorem, namely, (v)  if r(a, b)＝0，a＜b, then there exists c(a＜c＜b) such that　r(c, c)＝0，(vi)　foｒ ａ,ｂ(a＜b), there exists c(a＜c＜b) such that r(a, b)＝r(c, c).The purpose of this note is to point out that if r(x, y) satisfies (i), (ii), (iii), then we have (iv), (v), (vi) and Cauchy's theorem, namely,(vii)　if a function s(x, y) satisfies (i), (ii), (iii) and s(x, y)≠0, (a≦x, y≦b)　　　for a＜b, then there exists c(a＜c＜b) such that (r(a, b))/(s(a, b)) = (r(c, c))/(s(c, c)).","subitem_description_type":"Abstract"}]},"item_2_publisher_32":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"北見工業大学"}]},"item_2_select_15":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_select_item":"publisher"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"ISOBE, Kiro"}],"nameIdentifiers":[{"nameIdentifier":"32464","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-11-22"}],"displaytype":"detail","filename":"7-2-13.pdf","filesize":[{"value":"1.1 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"7-2-13.pdf","url":"https://kitami-it.repo.nii.ac.jp/record/6402/files/7-2-13.pdf"},"version_id":"574cb933-32b0-4005-9fa3-837a923accb3"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"A Certain Consideration on Derivatives and Rolle's Theorem","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"A Certain Consideration on Derivatives and Rolle's Theorem"}]},"item_type_id":"2","owner":"1","path":["23"],"pubdate":{"attribute_name":"公開日","attribute_value":"2007-04-09"},"publish_date":"2007-04-09","publish_status":"0","recid":"6402","relation_version_is_last":true,"title":["A Certain Consideration on Derivatives and Rolle's Theorem"],"weko_creator_id":"1","weko_shared_id":3},"updated":"2022-12-13T02:19:44.967263+00:00"}