Unified treatment of fractional integral inequalities via linear functionals

In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and H\" older type functions etc. These results give us an elegant method for obtaining a number of inequalities for various kinds of fractional integral operators such as for the Riemann-Liouville fractional integral operator, the Hadamard fractional integral operator, fractional hyperqeometric integral and corresponding q-integrals

Dokazi i primjene AG nejednakosti

Nejednakost između aritmetičke i geometrijske sredine, ili kraće AG nejednakost, svakako je jedna od najpoznatijih algebarskih nejednakosti. U literaturi se mogu naći deseci različitih dokaza ove nejednakosti, a u ovom članku promatramo razne vizualne dokaze. Osim toga pokazujemo neke primjene AG nejednakosti: određivanje maksimuma polinoma, računanje jednog limesa i dokaz Hölderove nejednakosti

On convexity-like inequalities (II)

We improve the classical Jensen inequality for convex functions by extending it to a wider class of functions. We also consider some weaker conditions for the weights occurring in this inequality

Dokazi bez riječi, 64 = 65 i zlatni rez

U ovom članku prikazujemo vizualni "dokaz" da je 64 = 65, objašnjavamo u čemu je greška i uspostavljamo vezu sa zlatnim rezom

Dokazi bez riječi, 64 = 65 i zlatni rez

U ovom članku prikazujemo vizualni "dokaz" da je 64 = 65, objašnjavamo u čemu je greška i uspostavljamo vezu sa zlatnim rezom

Some new refinements of the Young, Hölder, and Minkowski inequalities

We prove and discuss some new refined Hölder inequalities for any p> 1 and also a reversed version for 0 < p< 1. The key is to use the concepts of superquadraticity, strong convexity, and to first prove the corresponding refinements of the Young and reversed Young inequalities. Refinements of the Minkowski and reversed Minkowski inequalities are also given.