2018
Том 70
№ 8

Pečarić J. E.

Articles: 4
Article (English)

Generalizations of Sherman’s inequality via Fink’s identity and Green’s function

Ukr. Mat. Zh. - 2018. - 70, № 8. - pp. 1033-1043

New generalizations of Sherman’s inequality for $n$-convex functions are obtained by using Fink’s identity and Green’s function. By using inequalities for the Chebyshev functional, we establish some new Ostrowski- and Gruss-type inequalities related to these generalizations.

Article (English)

Refinements of Jessen’s functional

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 879-896

We obtain new refinements of Jessen’s functional defined by means of positive linear functionals. The accumulated results are then applied to weighted generalized and power means. We also obtain new refinements of numerous classical inequalities such as the arithmetic-geometric mean inequality, Young’s inequality, and H¨older’s inequality.

Article (English)

Generalizations of Steffensen’s Inequality by Lidstone’s Polynomials

Ukr. Mat. Zh. - 2015. - 67, № 11. - pp. 1525-1539

We obtain generalizations of Steffensen’s inequality by using Lidstone’s polynomials. Furthermore, the functionals associated with the obtained generalizations are used to generate n-exponentially and exponentially convex functions, as well as the new Stolarsky-type means.

Article (Ukrainian)

Certain inequalities for concave functions and concave sequences

Ukr. Mat. Zh. - 1981. - 33, № 5. - pp. 660—664