{"id":21598,"date":"2024-07-10T01:52:19","date_gmt":"2024-07-09T23:52:19","guid":{"rendered":"https:\/\/www.pmfst.unist.hr\/znanost\/?p=21598"},"modified":"2024-12-06T13:43:20","modified_gmt":"2024-12-06T12:43:20","slug":"grupa-za-matematicke-nejednakosti-i-primjene-2","status":"publish","type":"post","link":"https:\/\/www.pmfst.unist.hr\/znanost\/grupa-za-matematicke-nejednakosti-i-primjene-2\/","title":{"rendered":"Grupa za matemati\u010dke nejednakosti i primjene"},"content":{"rendered":"
[vc_row][vc_column width=”1\/4″][mk_title_box color=”#1e73be” margin_bottom=”0″ font_family=”none”]Voditelj grupe<\/b>[\/mk_title_box][mk_employees style=”boxed” column=”1″ employees=”18871″][\/vc_column][vc_column width=”3\/4″][mk_title_box color=”#1e73be” margin_bottom=”0″ font_family=”none”]\u010clanovi grupe<\/b>[\/mk_title_box][mk_custom_box padding_vertical=”10″][mk_custom_list style=”mk-moon-user-3″]\n
    \n
  • \u00a0 \u00a0<\/span>Milica Klari\u010di\u0107 Bakula<\/li>\n<\/ul>\n[\/mk_custom_list][\/mk_custom_box][\/vc_column][\/vc_row][vc_row][vc_column][mk_title_box color=”#1e73be” font_family=”none”]Odjel\/Katedra: <\/strong><\/p>\n

    Odjel za matematiku[\/mk_title_box][vc_column_text css=”.vc_custom_1520591712979{margin-bottom: 0px !important;}”]\n

    Opis istra\u017eivanja:<\/strong><\/h4>\n

    Koriste\u0107i identitet sa Greenovom funkcijom poku\u0161at \u0107emo generalizirati Levin-Ste\u010dkinovu nejednakost kao posljedicu rezultata za razliku integralnih aritmeti\u010dkih sredina sa razli\u010ditim mjerama pod uobi\u010dajenim uvjetima za Levin-Ste\u010dkinove nejednakosti. Kao specijalan slu\u010daj, poku\u0161at \u0107emo se dobiti jednu generalizaciju Levin-Ste\u010dkinove nejednakosti. Tako\u0111er, dokazat \u0107emo da se rezultat za op\u0107e mjere mo\u017ee jednostavno reducirati na slabije uvjete. Prou\u010davat \u0107e se generalizacije i profinjenja Clausingove nejednakosti kori\u0161tenjem op\u0107e simetri\u010dne Lebesgue-Stieltjes mjere na kona\u010dnim intervalima u R. U slu\u010daju apsolutno neprekidnih mjera dobivaju se najbolje mogu\u0107e aproksimacije. Identitet sa Greenovom funkcijom se pokazuje kao iznena\u0111uju\u0107e efikasan za dobivanje uvjeta, kriterija, primjera i kontraprimjera za obje strane Clausingove nejednakosti. Zanimljivo je da je pojam stroge konkavnosti i generalizirane stroge konkavnosti jako slabo obra\u0111en u literaturi, za razliku od stroge konveksnosti i generalizirane stroge konveksnosti. Koriste\u0107i rezultat o karakterizaciji generalizirane stroge konkavnosti (za realne funkcije realne varijable) istra\u017eivat \u0107e se generalizacije obje strane Clausingove nejednakosti za generalizirane strogo konkavne funkcije, iz \u010dega se mo\u017ee dobiti profinjenje obje strane Clausingove nejednakosti za konkavne funkcije.
    \nU planu je i prou\u010davanje pojmova generalizirane stroge konveksnosti i konkavnosti, te neprekidne simetrizacije.
    \nDrugi smjer istra\u017eivanja jest postavljanje gornjih me\u0111a za \u010cebi\u0161evljev funkcional pod raznim uvjetima, posebno onima koji dozvoljavaju negativne te\u017eine (Steffensenovim uvjetima). Takvi rezultati mogu kao poseban slu\u010daj dati nove gornje me\u0111e za Jensenovu nejednakost koje su pod slabijim uvjetima od onih klasi\u010dnih.<\/p>\n[\/vc_column_text][vc_column_text css=”.vc_custom_1520591959083{margin-bottom: 0px !important;}”]\n

    Partnerski potencijali:<\/strong><\/h4>\n

    Sveu\u010dili\u0161te u Zagrebu<\/p>\n[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text css=”.vc_custom_1520603890149{margin-bottom: 0px !important;}”]\n

    Financijski i drugi potencijali:<\/strong><\/h4>\n

    glavarine M. Klari\u010di\u0107 Bakula i J. Peri\u0107<\/p>\n[\/vc_column_text][vc_column_text css=”.vc_custom_1726611524227{margin-bottom: 0px !important;}”]Znanstveni ciljevi<\/strong> kojima se daje doprinos: Z-4, Z-8, Z-10<\/p>\n

    Mjerljivi pokazatelji<\/strong> kojima se daje doprinos i vrijednost doprinosa: R-Z-03, R-Z-F2, R-Z-F5, R-Z-F10[\/vc_column_text][\/vc_column][\/vc_row][vc_column][\/vc_column]\n<\/div>","protected":false},"excerpt":{"rendered":"

    [vc_row][vc_column width=”1\/4″][mk_title_box color=”#1e73be” margin_bottom=”0″ font_family=”none”]Voditelj grupe[\/mk_title_box][mk_employees style=”boxed” column=”1″ employees=”18871″][\/vc_column][vc_column width=”3\/4″][mk_title_box color=”#1e73be” margin_bottom=”0″ font_family=”none”]\u010clanovi grupe[\/mk_title_box][mk_custom_box padding_vertical=”10″][mk_custom_list style=”mk-moon-user-3″] \u00a0 \u00a0Milica Klari\u010di\u0107 Bakula [\/mk_custom_list][\/mk_custom_box][\/vc_column][\/vc_row][vc_row][vc_column][mk_title_box color=”#1e73be” font_family=”none”]Odjel\/Katedra: Odjel za matematiku[\/mk_title_box][vc_column_text css=”.vc_custom_1520591712979{margin-bottom: 0px !important;}”] Opis istra\u017eivanja: Koriste\u0107i identitet sa Greenovom funkcijom poku\u0161at \u0107emo generalizirati Levin-Ste\u010dkinovu nejednakost kao posljedicu rezultata za razliku integralnih aritmeti\u010dkih sredina sa razli\u010ditim mjerama pod uobi\u010dajenim uvjetima […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"rs_blank_template":"","rs_page_bg_color":"","slide_template_v7":"","footnotes":""},"categories":[158,149],"tags":[],"poredak":[],"class_list":["post-21598","post","type-post","status-publish","format-standard","hentry","category-istrazivacke-grupe-odjela-za-matematiku","category-nove-istrazivacke-grupe"],"acf":[],"yoast_head":"\nGrupa za matemati\u010dke nejednakosti i primjene - Znanstvena djelatnost, PMF Split<\/title>\n<meta name=\"robots\" content=\"noindex, follow\" \/>\n<meta property=\"og:locale\" content=\"hr_HR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Grupa za matemati\u010dke nejednakosti i primjene - Znanstvena djelatnost, PMF Split\" \/>\n<meta property=\"og:description\" content=\"[vc_row][vc_column width=”1\/4″][mk_title_box color=”#1e73be” margin_bottom=”0″ font_family=”none”]Voditelj grupe[\/mk_title_box][mk_employees style=”boxed” column=”1″ employees=”18871″][\/vc_column][vc_column width=”3\/4″][mk_title_box color=”#1e73be” margin_bottom=”0″ font_family=”none”]\u010clanovi grupe[\/mk_title_box][mk_custom_box padding_vertical=”10″][mk_custom_list style=”mk-moon-user-3″] \u00a0 \u00a0Milica Klari\u010di\u0107 Bakula [\/mk_custom_list][\/mk_custom_box][\/vc_column][\/vc_row][vc_row][vc_column][mk_title_box color=”#1e73be” font_family=”none”]Odjel\/Katedra: Odjel za matematiku[\/mk_title_box][vc_column_text css=”.vc_custom_1520591712979{margin-bottom: 0px !important;}”] Opis istra\u017eivanja: Koriste\u0107i identitet sa Greenovom funkcijom poku\u0161at \u0107emo generalizirati Levin-Ste\u010dkinovu nejednakost kao posljedicu rezultata za razliku integralnih aritmeti\u010dkih sredina sa razli\u010ditim mjerama pod uobi\u010dajenim uvjetima […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.pmfst.unist.hr\/znanost\/grupa-za-matematicke-nejednakosti-i-primjene-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Znanstvena djelatnost, PMF Split\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/pmfst\/\" \/>\n<meta property=\"article:published_time\" content=\"2024-07-09T23:52:19+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-12-06T12:43:20+00:00\" \/>\n<meta name=\"author\" content=\"autor\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@PmfSplit\" \/>\n<meta name=\"twitter:site\" content=\"@PmfSplit\" \/>\n<meta name=\"twitter:label1\" content=\"Napisao\/la\" \/>\n\t<meta name=\"twitter:data1\" content=\"autor\" \/>\n\t<meta name=\"twitter:label2\" content=\"Procijenjeno vrijeme \u010ditanja\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.pmfst.unist.hr\\\/znanost\\\/grupa-za-matematicke-nejednakosti-i-primjene-2\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.pmfst.unist.hr\\\/znanost\\\/grupa-za-matematicke-nejednakosti-i-primjene-2\\\/\"},\"author\":{\"name\":\"autor\",\"@id\":\"https:\\\/\\\/www.pmfst.unist.hr\\\/znanost\\\/#\\\/schema\\\/person\\\/8c4957fe31fd46303be41a1bd068040a\"},\"headline\":\"Grupa za matemati\u010dke nejednakosti i primjene\",\"datePublished\":\"2024-07-09T23:52:19+00:00\",\"dateModified\":\"2024-12-06T12:43:20+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.pmfst.unist.hr\\\/znanost\\\/grupa-za-matematicke-nejednakosti-i-primjene-2\\\/\"},\"wordCount\":463,\"publisher\":{\"@id\":\"https:\\\/\\\/www.pmfst.unist.hr\\\/znanost\\\/#organization\"},\"articleSection\":[\"Istra\u017eiva\u010dke grupe odjela za matematiku\",\"Nove istra\u017eiva\u010dke grupe\"],\"inLanguage\":\"hr\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.pmfst.unist.hr\\\/znanost\\\/grupa-za-matematicke-nejednakosti-i-primjene-2\\\/\",\"url\":\"https:\\\/\\\/www.pmfst.unist.hr\\\/znanost\\\/grupa-za-matematicke-nejednakosti-i-primjene-2\\\/\",\"name\":\"Grupa za matemati\u010dke nejednakosti i primjene - 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