Title: General inequalities and applications
Project funding: Croatian Ministry of Science, Education and Sports
Project Leader: Academician Prof. Josip Pečarić, Ph.D.
Faculty of Textile Technology is a holder of the program "Mathematical inequalities and applications", on which there are 5 projects from the Universities in Zagreb and Split. One of these projects is the project "General inequalities and applications".
The main purpose of the research is the contribution to the development of the theory of inequalities and its integration in the contemporary trends in mathematics. Our aim is to build the competent team of researchers whose relevant results and collaboration with the experts (domestic and foreign) in other fields, will contribute to the promotion of Croatian mathematics in the world.
The concrete aim of our research is to accomplish the further progress in the research of the following important directions: generalizations, refinements and improvements of some classical inequalities; inequalities in more complex abstract algebraic and geometric structures; different terms of convex functions and connected inequalities; inequalities in numerical analysis, especially their applications in numerical integration and in interpolation schemes. It is expected the significant contribution to the world science in the theory of inequalities through the improvements, interpolations, generalizations of the general inequalities, like the Hardy, Hölder and Čebišev inequality, the inequalities for means, especially for their converse inequalities, the Jensen and other inequalities for real or operator convex functions, the Cauchy, Kantorovič, Opial, Hilbert and Grüss inequality, inequalities in n-normalized spaces, inequalities for simplexes, integral inequalities and others.
Until now, our activity led to 4 new mathematical journals, from which the journal "Mathematical inequalities and applications" was the first Croatian mathematical journal indexed by SCIE list, while the journal "Operators and matrices" is the only Croatian mathematical journal indexed by SCIE and CC list, and that was from its first number.
Within the project there were organized two international mathematical conferences: "Mathematical Inequalities and Applications 2008" (MIA 2008) which was held in Trogir, Croatia, and "Mathematical Inequalities and Applications 2010" (MIA 2010) in Lahore, Pakistan. The conference "Mathematical Inequalities and Applications 2008" was held in honour of Academician Josip Pečarić on the occasion of his 60th birthday. In that conference were given 15 plenary lectures and more than 120 short communications, and there participated the mathematicians from all over the world. The talks from the conference are published in two issues of the "Journal of mathematical inequalities" and in one issue of the journal "Mathematical inequalities and applications".
The members of the project are authors and co-authors of more than 800 scientific papers (already published or accepted) as well as 15 monographs (7 in English language). More than 320 papers are published in journals indexed by SCIE list, and more than 160 in CC journals. Members of the project collaborate with more than 170 mathematicians from Croatia and abroad (from 30 countries). This work has resulted with 26 new Ph.D. of mathematical sciences in Croatia and 6 abroad.
Mathematicians from this project are members of the Editorial boards in about 20 mathematical journals, reviewers in more than 70 mathematical journals, reviewers of books published by well-known publishing houses, and very often are members of Scientific boards of international mathematical conferences, invited or plenary speakers, as well as members of the Committees for Ph.D. at home and abroad.
One issue of the "Banach Journal of Mathematical Analysis" (SCIE and CC journal) is dedicated to Academician Josip Pečarić.