Popoviciu type inequalities for n-convex functions via extension of Montgomery identity

Asif R. Khan; Josip Pečarić; Marjan Praljak

doi:10.1515/auom-2016-0053

.blurhash-client-img { display: none !important; }

Popoviciu type inequalities for n-convex functions via extension of Montgomery identity

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 24 (2016): Issue 3 (November 2016)

By: Asif R. Khan, Josip Pečarić and Marjan Praljak

Open Access

|Sep 2017

Abstract

Extension of Montgomery's identity is used in derivation of Popoviciu-type inequalities containing sums , where f is an n-convex function. Integral analogues and some related results for n-convex functions at a point are also given, as well as Ostrowski-type bounds for the integral remainders of identities associated with the obtained inequalities.

References

[1] A. Aglić Aljinović, J. Pečarić, and A. Vukelić, On some Ostrowski type inequalities via Montgomery identity and Taylor's formula II, Tamkang Jour. Math. 36 (4), (2005), 279-301.10.5556/j.tkjm.36.2005.100
Search in Google Scholar Back to article
[2] I. A. Baloch, J. Pečarić and M. Praljak, Generalization of Levinson's inequality, J. Math. Inequal. 9 (2015), 571-586.10.7153/jmi-09-49
Search in Google Scholar Back to article
[3] S. N. Bernstein, Sur les fonctions absolument monotones, Acta Math. 52 (1) (1929), 1-66.10.1007/BF02592679
Search in Google Scholar Back to article
[4] P. Cerone and S. S. Dragomir, Some new Owstrowski-type bounds for the Čebyšev functional and applications, J. Math. Inequal., 8(1) (2014), 159-170.10.7153/jmi-08-10
Search in Google Scholar Back to article
[5] J.Jakšetić and J. Pečarić, Exponential convexity method, J. Convex Anal., 20 (1) (2013), 181-197.
Search in Google Scholar Back to article
[6] D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Inequalities for functions and their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1994.
Search in Google Scholar Back to article
[7] J. Pečarić, On Jessens Inequality for Convex Functions, III, J. Math. Anal. Appl., 156 (1991), 231-239.10.1016/0022-247X(91)90393-E
Search in Google Scholar Back to article
[8] J. Pečarić and J. Perić, Improvements of the Giaccardi and the Petrović inequality and related Stolarsky type means, An. Univ. Craiova Ser. Mat. Inform., 39 (1) (2012), 65-75.
Search in Google Scholar Back to article
[9] J. Pečarić, M. Praljak and A. Witkowski, Linear operator inequality for n-convex functions at a point, Math. Ineq. Appl. 18 (2015), 1201-1217.10.7153/mia-18-93
Search in Google Scholar Back to article
[10] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex functions, partial orderings and statistical applications, Academic Press, New York, 1992.
Search in Google Scholar Back to article
[11] T. Popoviciu, Notes sur les fonctions convexes d'orde superieur III, Mathematica (Cluj) 16, (1940), 74-86.
Search in Google Scholar Back to article
[12] T. Popoviciu, Notes sur les fonctions convexes d'orde superieur IV, Disqusitiones Math. 1, (1940), 163-171.
Search in Google Scholar Back to article
[13] T. Popoviciu, Notes sur les fonctions convexes d'orde superieur IX, Bull. Math. Soc. Roumaine Sci. 43, (1941), 85-141.
Search in Google Scholar Back to article
[14] T. Popoviciu, Les fonctions convexes, Herman and Cie, Editeurs, Paris 1944.
Search in Google Scholar Back to article
[15] D. V. Widder, Necessary and sućient conditions for the representation of a function by a doubly infinite Laplace integral, Bull. Amer. Math. Soc., 40 (4) (1934), 321-326.10.1090/S0002-9904-1934-05862-2
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/auom-2016-0053 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 161 - 188

Submitted on: Sep 9, 2015

Accepted on: Feb 12, 2016

Published on: Sep 21, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

n-convex functions,

n-convex functions at a point,

Montgomery identity,

Čebyšev functional,

exponential convexity.

Related subjects:

Mathematics,

General mathematics

© 2017 Asif R. Khan, Josip Pečarić, Marjan Praljak, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 24 (2016): Issue 3 (November 2016)