{"id":1243,"date":"2018-03-15T12:37:03","date_gmt":"2018-03-15T11:37:03","guid":{"rendered":"https:\/\/www.pmfst.unist.hr\/znanost\/?p=1243"},"modified":"2025-12-08T10:52:56","modified_gmt":"2025-12-08T09:52:56","slug":"grupa-za-matematicke-nejednakosti-i-primjene","status":"publish","type":"post","link":"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-matematicke-nejednakosti-i-primjene\/","title":{"rendered":"Grupa za matemati\u010dke nejednakosti i primjene"},"content":{"rendered":"
[vc_row][vc_column width=”1\/3″][mk_title_box color=”#1e73be” font_family=”none”]Voditeljica grupe<\/b>[\/mk_title_box][mk_employees column=”1″ custom_image_size=”true” image_width=”250″ image_height=”250″ rounded_image=”false” grayscale_image=”false” count=”-1″ employees=”11936″][mk_title_box color=”#1e73be” font_family=”none”]\u010clanovi grupe<\/b>[\/mk_title_box][mk_employees column=”1″ custom_image_size=”true” image_width=”250″ image_height=”250″ rounded_image=”false” grayscale_image=”false” count=”-1″ employees=”11941″][\/vc_column][vc_column width=”2\/3″][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

Podru\u010dje istra\u017eivanja:<\/h4>\n

Matemati\u010dke nejednakosti i njihove primjene u numeri\u010dkoj analizi, poop\u0107enja konveksnosti i primjene
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Opis istra\u017eivanja:<\/h4>\n

Ustanovljuju se nove op\u0107e metode za pobolj\u0161avanje nekih od klasi\u010dnih nejednakosti za konveksne funkcije kao \u0161to su Hermite-Hadamardove nejednakosti, Jensenova nejednakost i suprotna Jensenova nejednakost. Kao posebni slu\u010dajevi spomenutih pobolj\u0161anja mogu se, izme\u0111u ostaloga, dobiti profinjenja suprotne H\u00f6lderove nejednakosti i suprotne nejednakosti Minkowskoga. Dobivena pobolj\u0161anja Jensenove i suprotne Jensenove nejednakosti koriste se i za uspostavljanje novih nejednakosti vezanih uz Shannonovu entropiju i Zipf-Mandelbrotov zakon koji, kao \u0161to je dobro poznato, imaju zna\u010dajnu primjenu u informacijskim znanostima. Istra\u017euju se razne klase poop\u0107enih konveksnih funkcija kao i klase funkcija koje generiraju o\u0161trije varijante klasi\u010dnih nejednakosti od klase konveksnih funkcija, kao \u0161to su superkvadratne funkcije i jako konveksne funkcije. Poku\u0161at \u0107e se uspostaviti i neke nove integralne nejednakosti koje omogu\u0107avaju postavljanje boljih ocjena za pogre\u0161ke korigiranih kvadraturnih formula.
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Kontakti s akademskim i drugim institucijama:<\/strong><\/h4>\n

1. Prirodoslovno-matemati\u010dki fakultet Sveu\u010dili\u0161ta u Zagrebu
\n2. Tekstilno-tehnolo\u0161ki fakultet Sveu\u010dili\u0161ta u Zagrebu
\n3. Fakultet strojarstva i brodogradnje Sveu\u010dili\u0161ta u Zagrebu
\n4. Matemati\u010dki odjel Sveu\u010dili\u0161ta u Osijeku
\n5. Department of Mathematics, University of Bielsko-Biala, Poland
\n6. Department of Mathematics, University of Debrecen, Hungary
\n7. Department of Mathematics, University of Haifa, Israel
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Opis dosada\u0161nje suradnje:<\/strong><\/h4>\n

Suradnja se najvi\u0161e o\u010dituje u objavljivanju zajedni\u010dkih radova no provodi se i kroz sudjelovanja na konferencijama i simpozijima koje su spomenute istra\u017eiva\u010dke grupe organizirale u Hrvatskoj, Poljskoj i Ma\u0111arskoj te u zajedni\u010dkim seminarima kroz ERASMUS+ mobilnost.
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Planovi budu\u0107ih istra\u017eivanja:<\/strong><\/h4>\n

Nastavljaju se prethodno spomenuta istra\u017eivanja.[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text css=”.vc_custom_1763552892611{margin-bottom: 0px !important;}”]Popis odabranih znanstvenih radova:<\/strong><\/p>\n

    \n
  1. I. Butt, M. Klari\u010di\u0107 Bakula, J. Pe\u010dari\u0107, Steffensen-Gr\u00fcss inequality, Journal of Mathematical Inequalities, Vol. 14, Issue 2 (2021), 799-810.<\/li>\n
  2. Klari\u010di\u0107 Bakula, J. Pe\u010dari\u0107, Chebyshev-Steffensen inequality involving the inner product, Mathematics, Vol. 10, Issue 1 (2022), 122.<\/li>\n
  3. Klari\u010di\u0107 Bakula, K. Nikodem, Ohlin type theorem and its applications for strongly convex set-valued maps, Journal of Convex Analysis, Vol. 10, Issue 1 (2022), 221\u2013229.<\/li>\n
  4. W. Alomari, M. Klari\u010di\u0107 Bakula, An Application of Hayashi’s Inequality for Differentiable Functions, Mathematics, Vol. 10, Issue 6 (2022), 907.<\/li>\n
  5. Adamek, M. Klari\u010di\u0107 Bakula, K. Nikodem, Strong Schur-convexity of the integral mean, Results in Mathematics, Vol. 78, Issue 2 (2023), 58.<\/li>\n
  6. Klari\u010di\u0107 Bakula, J. Pe\u010dari\u0107, New upper bounds for the weighted Chebyshev functional, Annales Mathematicae Silesianae,\u00a0Vol. 38, Issue 1 (2024), 37\u201356.<\/li>\n
  7. S. I. Butt, M. Klari\u010di\u0107 Bakula, \u0110. Pe\u010dari\u0107, J. Pe\u010dari\u0107, Jensen-Gr\u00fcss inequality and its applications for the Zipf-Mandelbrot law, Mathematical Methods in the Applied Sciences, Vol.44, Issue 2 (2021), 1664-1673.<\/li>\n
  8. Pe\u010dari\u0107, Josip; Peri\u0107, Jurica. Refinements of the integral form of Jensen\u2019s and the Lah\u2013Ribari\u010d inequalities and applications for Csisz\u00e1r divergence. Journal of inequalities and applications. 2020 (2020), 1; 108.<\/li>\n
  9. M. Klari\u010di\u0107 Bakula, J. Pe\u010dari\u0107 , On the pre-Jensen-Gr\u00fcss inequality, Mathematical Inequalities and Applications, Vol.23, Issue 4 (2020), 1529-1543.<\/li>\n
  10. M. Klari\u010di\u0107 Bakula, K. Nikodem, Converse Jensen inequality for strongly convex set-valued maps, Journal of Mathematical Inequalities, Vol. 12, Issue 2 (2018), 545-550.<\/li>\n
  11. M. Klari\u010di\u0107 Bakula, Jensen-Steffensen inequality for strongly convex functions, Journal of Inequalities and Applications, Vol. 2018, Article 306 (2018) 1-12.<\/li>\n
  12. Pe\u010dari\u0107, Josip; Peri\u0107, Jurica. New improvement of the converse Jensen inequality. Mathematical inequalities & applications. 21 (2018), 1; 217-234.<\/li>\n
  13. Klari\u010di\u0107 Bakula, Milica; Nikodem, Kazimierz. On the converse Jensen inequality for strongly convex functions. Journal of mathematical analysis and applications. 434 (2016) , 1; 516-522.<\/li>\n
  14. Bani\u0107, Senka; Klari\u010di\u0107 Bakula, Milica. Jensen’s inequality for functions superquadratic on the coordinates. Journal of Mathematical Inequalities. 9 (2015) , 4; 1365-1375.<\/li>\n
  15. Klari\u010di\u0107 Bakula, Milica; Pe\u010dari\u0107, Josip; Ribi\u010di\u0107 Penava, Mihaela; Vukeli\u0107, Ana. New estimations of the remainder in three-point quadrature formulae of Euler type. Journal of Mathematical Inequalities. 9 (2015) , 4; 1143-1156.<\/li>\n
  16. Klari\u010di\u0107 Bakula, Milica; Pe\u010dari\u0107, Josip; Ribi\u010di\u0107 Penava, Mihaela; Vukeli\u0107, Ana. Some Gr\u00fcss type inequalities and corrected three-point quadrature formulae of Euler type. Journal of inequalities and applications. (2015) ; 76-1-76-14.<\/li>\n
  17. Bibi, Rabia; Pe\u010dari\u0107, Josip; Peri\u0107, Jurica. Improvements of the Hermite–Hadamard inequality on time scales. Journal of mathematical inequalities. 9 (2015) , 3; 913-934.<\/li>\n
  18. Matkovi\u0107, Anita; Pe\u010dari\u0107, Josip; Peri\u0107, Jurica. A refinement of the Jessen-Mercer inequality and a generalization on convex hulls in R^k. Journal of Mathematical Inequalities. 9 (2015) , 4; 1093-1114.<\/li>\n
  19. Klari\u010di\u0107 Bakula, Milica. An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates. The Australian journal of mathematical analysis and applications. 11 (2014) , 1; 1-7.<\/li>\n
  20. Klari\u010di\u0107 Bakula, Milica; Pe\u010dari\u0107, Josip; Ribi\u010di\u0107 Penava, Mihaela; Vukeli\u0107, Ana. Some inequalities for the \u010ceby\u0161ev functional and general four-point quadrature formulae of Euler type. Matemati\u010dki bilten. 38 (2014) , 2; 69-80.<\/li>\n
  21. Klari\u010di\u0107 Bakula, Milica; Pe\u010dari\u0107, Josip; Ribi\u010di\u0107 Penava, Mihaela. General quadrature formulae based on the weighted Montgomery identity and related inequalities. Rad Hrvatske akademije znanosti i umjetnosti. Razred za matemati\u010dke, fizi\u010dke i kemijske znanosti. Matemati\u010dke znanosti. 17 (2013) ; 139-150.<\/li>\n
  22. Mi\u0107i\u0107, Jadranka; Pe\u010dari\u0107 Josip; Peri\u0107, Jurica. Refined converses of Jensen’s operator inequality. Journal of inequalities and applications. (2013) , 353; 1-16.<\/li>\n
  23. Mi\u0107i\u0107, Jadranka; Pe\u010dari\u0107, Josip; Peri\u0107, Jurica. Refined Jensen’s operator inequality with condition on spectra. Operators and matrices. 7 (2013) , 2; 293-308.<\/li>\n
  24. Pe\u010dari\u0107, Josip; Peri\u0107, Jurica. Generalizations and improvements of converse Jensen’s inequality for convex hulls in R^k. Mathematical inequalities and applications. 17 (2013) ; 1125-1137.<\/li>\n
  25. Mi\u0107i\u0107, Jadranka; Pe\u010dari\u0107, Josip; Peri\u0107, Jurica. Extension of the refined Jensen’s operator inequality with condition on spectra. Annals of Functional Analysis. 3 (2012) , 1; 67-85.<\/li>\n
  26. Klari\u010di\u0107 Bakula, Milica; Pe\u010dari\u0107, Josip; Peri\u0107, Jurica. Extensions of the Hermite-Hadamard inequality with applications. Mathematical inequalities and applications. 15 (2012) , 4; 899-921.<\/li>\n
  27. Pe\u010dari\u0107, Josip; Peri\u0107, Jurica. Remarks on the paper “Jensen’s inequality and new entropy bounds” of S. Simi\u0107. Journal of mathematical inequalities. 6 (2012) , 4; 631-636.<\/li>\n
  28. Klari\u010di\u0107 Bakula, Milica; Pe\u010dari\u0107, Josip; Peri\u0107, Jurica. On the converse Jensen inequality. Applied mathematics and computation. 218 (2012) , 11; 6566-6575.<\/li>\n
  29. Iveli\u0107, Slavica; Klari\u010di\u0107 Bakula, Milica; Pe\u010dari\u0107, Josip. Converse Jensen-Steffensen inequality. Aequationes mathematicae. 82 (2011) , 3; 233-246.<\/li>\n
  30. Klari\u010di\u0107 Bakula, Milica; Mati\u0107, Marko; Pe\u010dari\u0107, Josip. Generalizations of the Jensen-Steffensen and related inequalities. Central European Journal of Mathematics. 7 (2009) , 4; 787-803.<\/li>\n
  31. Klari\u010di\u0107 Bakula, Milica; Ribi\u010di\u0107 Penava, Mihaela. General four-point quadrature formulae with applications for \u03b1-L-H\u00f6lder type functions. Journal of mathematical ineqalities. 3 (2009) , 3; 427-436.<\/li>\n
  32. Kirmaci, U.S.; Klari\u010di\u0107 Bakula, Milica; \u00d6zdemir, M.E.; Pe\u010dari\u0107, Josip. Hadamard-type inequalities for s-convex functions. Applied Mathematics and Computation. 193 (2007) , 1; 26-35.<\/li>\n<\/ol>\n[\/vc_column_text][\/vc_column][\/vc_row]\n<\/div>","protected":false},"excerpt":{"rendered":"

    [vc_row][vc_column width=”1\/3″][mk_title_box color=”#1e73be” font_family=”none”]Voditeljica grupe[\/mk_title_box][mk_employees column=”1″ custom_image_size=”true” image_width=”250″ image_height=”250″ rounded_image=”false” grayscale_image=”false” count=”-1″ employees=”11936″][mk_title_box color=”#1e73be” font_family=”none”]\u010clanovi grupe[\/mk_title_box][mk_employees column=”1″ custom_image_size=”true” image_width=”250″ image_height=”250″ rounded_image=”false” grayscale_image=”false” count=”-1″ employees=”11941″][\/vc_column][vc_column width=”2\/3″][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;}”] Podru\u010dje istra\u017eivanja: Matemati\u010dke nejednakosti i njihove primjene u numeri\u010dkoj analizi, poop\u0107enja konveksnosti i primjene [\/vc_column_text][vc_column_text css=”.vc_custom_1520591748316{margin-bottom: 0px !important;}”] Opis istra\u017eivanja: Ustanovljuju se […]<\/p>\n","protected":false},"author":1,"featured_media":1394,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"rs_blank_template":"","rs_page_bg_color":"","slide_template_v7":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-1243","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-odjel-za-matematiku-istrazivacka-grupa"],"acf":[],"yoast_head":"\nGrupa za matemati\u010dke nejednakosti i primjene - 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