The research group develops new theoretical and applied knowledge in the fields of mathematics, statistics, and information systems. Its activities focus on advancing mathematical inequalities and integral formulas for convex functions, investigating topological spaces through rough shape and finite rough shape theory, and developing the corresponding invariants. The group also applies advanced statistical methods to assess future extreme precipitation events and develops and validates extended technology acceptance models that incorporate organizational factors, user knowledge, and intelligent system features. In addition, the group conducts research in mathematics education, with a particular emphasis on diagnosing students’ misconceptions of key concepts and developing modern teaching methodologies.

• Convexity Theory and Functional Inequalities: Expertise in developing new classes of convex functions (harmonic, reciprocal, strong convexity) and deriving, generalizing, and improving fundamental inequalities (Jensen, Jensen-Mercer, Hermite-Hadamard), including their multidimensional extensions.
• Mathematical Analysis on Time Scales and Mean Value Theory: Experience in applying delta calculus and multiple Lebesgue delta integration to unify continuous and discrete models, as well as in the construction, characterization, and monotonicity analysis of new generalized means.
• Applications in Probability Theory: Development of inequalities for the expected value of random variables, analysis of probabilistic models using convexity methods and functional inequalities, and development of models for estimating future maximum short-duration precipitation values using extreme value theory.
• Applications in Information Theory: Expertise in deriving new bounds for Shannon entropy, f-divergences, and other information measures, including the development of new lower bounds and improvements of existing results.
• Multidimensional Analysis and Abstract Spaces: Development of results in general multidimensional settings and their applications in mathematical analysis, information theory, and related fields.
• Mathematics Education: Diagnosing students’ misconceptions of key mathematical concepts and developing contemporary teaching methods.
• Rough Shape and Finite Rough Shape Theory: Study of topological spaces within the framework of rough shape and finite rough shape theory, including rough shape and finite rough shape invariants. Investigation of finite rough shape path connectedness and characterization of finite rough shape isomorphisms.
• Technology Acceptance Models: Development and testing of extended TAM/UTAUT models in business and educational contexts.

Laboratories

• One laboratory (classroom) for organizing seminars and workshops

Equipment

• R, SPSS, Stata, Overleaf

• Climate and Extreme Weather Conditions in Croatia’s Natural and Urban Environments (IP-2022-10-4144)

The research group achieves scientific results through continuous collaboration with researchers from national and international universities and research institutions. Such cooperation includes the joint development of new theoretical results, preparation of scientific publications, application for and implementation of research projects, and the exchange of knowledge and research experience. The group is open to collaboration in the fields of mathematical analysis, convexity theory, functional inequalities, probability theory, information sciences, time scale theory, and other related areas. Particular emphasis is placed on interdisciplinary research that connects mathematical methods with applications in information theory, computer science, engineering, and other scientific disciplines. Collaboration opportunities include joint research projects, scientific publications, participation in national and international projects, organization of scientific conferences and workshops, researcher mobility programs, and mentoring of early-career researchers and doctoral students. Collaboration with higher education institutions and schools also includes projects aimed at improving teaching practices, curriculum development, and the implementation of modern e-learning tools in mathematics education.