Author:
Khan Asif R.,Pečarić Josip E.,Praljak Marjan
Abstract
Abstract
Using an extension of Montgomery’s identity and the Green’s function, we obtain new identities and related inequalities for weighted averages of n-convex functions, i.e. the sum $$\sum _{i=1}^m \rho _i h(\lambda _i)$$
∑
i
=
1
m
ρ
i
h
(
λ
i
)
and the integral $$\int ^{b}_{a} \rho (\lambda ) h(\gamma (\lambda ))d\lambda $$
∫
a
b
ρ
(
λ
)
h
(
γ
(
λ
)
)
d
λ
where h is an n-convex function.
Funder
Ministry of Education and Science of the Russian Federation
Publisher
Springer Science and Business Media LLC
Reference9 articles.
1. Aljinović, A.Aglić; Pečarić, J.; Vukelić, A.: On some Ostrowski type inequalities via Montgomery identity and Taylor’s formula II. Tamkang Jour. Math 36(4), 279–301 (2005)
2. Butt, S.I.; Pečarić, J.; Praljak, M.: Reversed Hardy inequality for $$C$$-monotone functions. J. Math. Inequal. 10(3), 603–622 (2016)
3. Cerone, P.; Dragomir, S.S.: Some new Ostrowski-type bounds for the Čebyšev functional and applications. J. Math. Inequal. 8(1), 159–170 (2014)
4. Mitrinović, D.S.; Pečarić, J.E.; Fink, A.M.: Inequalities for Functions and Their Integrals and Derivatives. Kluwer Academic Publishers, Dordrecht (1994)
5. Pečarić, J.: On Jessens inequality for convex functions. III. J. Math. Anal. Appl. 156, 231–239 (1991)
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