Mathematical Inequalities and Applications

group leader

izv. prof. dr. sc. Josipa Barić

Personal data  Bibliography  Teaching duties

associates

izv. prof. dr. sc. Anita Matković

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Ivana Grgić, prof.

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Marina Mandić, mag. math.

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Research Topics

  1. new estimates of Shannon’s entropy obtained from the known properties of superquadratic functions,
  2. new estimates of the relative entropy derived from Jensen’s inequality for superquadratic functions,
  3. applications of obtained results on the Zipf and Zipf-Mandelbrot law,
  4. introducing the new method in studing the weighted versions of integral identities using the harmonic sequences of polynomials and w-harmonic sequences of functions,
  5. refinements of the reverse Jensen-Mercer inequality,
  6. bounds for the Čebyšev’s functional in terms of Ostrowski inequality,
  7. bounds for the Jensen-Mercer functional in terms of Ostrowski inequality,
  8. point processes – random distribution of points in space. Points may represent times of events, locations of objects or elements of function space, while space is real line, Cartesian plane or general space,
  9. asymptotic expansions of function.

Description of Laboratory and Equipment

  • Offices (4) equipped with computers
  • Laboratory (1) used as classroom
project title

Mathematical inequalities and applications (MANETS)

Research project activities

Using Jensen’s inequality and the converse Jensen’s inequality for superquadratic functions we obtain new estimates for Shannon’s entropy of the random variable X and derive new lower and upper bounds for the Shannon entropy in the terms of the Zipf and Zipf – Mandelbrot’s law.

We will introduce the new method in studing the weighted versions of integral identities using the harmonic sequences of polynomials and w-harmonic sequences of functions.

By use of refinements of the reverse Jensen-Steffensen inequality we will obtain refinements of the reverse Jensen-Mercer inequality, under different conditions on weights and arguments.

Using Pečarić’s identity we will establish bounds for the Čebyšev’s functional of Mercer’s type, and by use of these bounds, we will establish bounds for the Jensen-Mercer functional in terms of Ostrowski inequality.