Naslov
Chebyshev and Gr\" uss type inequalities involving two linear functionals and applications

Autori
Nikolova, Ludmila ; Varošanec, Sanja

Izvornik
Mathematical inequalities & applications (1331-4343) 19 (2016), 1; 127-143

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
the Chebyshev inequality ; the Gr\

Sažetak
In the present paper we prove the Chebyshev inequality involving two isotonic linear functionals. Namely, if $A$ and $B$ are isotonic linear functionals, then $A(pfg)B(q)+A(p)B(qfg) \geq A(pf)B(qg)+A(pg)B(qf) $, where $p, q$ are non-negative weights and $f, g$ are similarly ordered functions such that the above-mentioned terms are well-defined. If functionals are equal, i.e. $A=B$ and if $p=q$, then the above inequality becomes the Chebyshev inequality involving one isotonic linear functional: $A(p) A(pfg) \geq A(pf)A(pg)$ in which we recognize a generalization of the well-known classical integral and discrete Chebyshev inequalites as special cases. We derive various properties of functionals related to the difference of the right-hand and the left-hand sides of the above-mentioned inequalities. The most remarkable results are the Gr\" uss type inequalities for two functionals. Inequalities involving some fractional integral operators are also given.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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