New proofs of Fejer's and discrete Hermite-Hadamard inequalities with applications-Reference-Cited by-同舟云学术

New proofs of Fejer's and discrete Hermite-Hadamard inequalities with applications

Published:2023-06-22 Issue:4 Volume:72 Page:1110-1125
ISSN:1303-5991
Container-title:Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
language:en
Short-container-title:Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

Author:

SEKİN Çağla¹^ORCID,TAMAR Mehmet Emin²^ORCID,ALİYEV İlham¹^ORCID

Affiliation:

1. AKDENIZ UNIVERSITY

2. ABDULLAH GUL UNIVERSITY

Abstract

New proofs of the classical Fejer inequality and discrete Hermite-Hadamard inequality (HH) are presented and several applications are given, including (HH)-type inequalities for the functions, whose derivatives have inflection points. Morever, some estimates from below and above for the first moments of functions $f:[a,b]\rightarrow \mathbb{R}$ about the midpoint $c=(a+b)/2$ are obtained and the reverse Hardy inequality for convex functions $f:(0,\infty )\rightarrow (0,\infty )$ is established.

Publisher

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

Subject

General Medicine

Reference22 articles.

1. Amrahov, S. E., A note on Hadamard inequalities for the product of the convex functions, International J. of Research and Reviews in Applied Sciences, 5(2) (2010), 168-170.

2. Alomari, M., Darus, M. and Dragomir, S. S., New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, Tamkang J. Math., 41(4) (2010), 353-359.

3. Azpetia, A. G., Convex functions and the Hadamard inequality, Revista Colombiana Mat., 28 (1994), 7-12.

4. Bakula, M. K., Özdemir, M. E. and Pecaric, J., Hadamard-type inequalities for m-convex and $(\alpha,m)$-convex functions. J. Ineq. Pure Appl. Math., 9(4) (2008), Article 96.

5. Chen, F., Liu, X., On Hermite-Hadamard type inequalities for functions whose second derivatives absolute values are s-convex, ISRN Applied Mathematics, (2014), 1-4, DOI:10.1155/2014/829158.