Cauchy-Type Means and Exponential and Logarithmic Convexity for Superquadratic Functions on Time Scales

Author

Rabia Bibi
Martin Bohner, Missouri University of Science and TechnologyFollow
Josip Pecaric

Abstract

In this paper, we define positive functionals by using the Jensen's inequality, converse of Jensen's inequality, and Jensen-Mercer's inequality on time scales for superquadratic functions. We give mean-value theorems and introduce related Cauchy-type means by using the functionals mentioned above and show the monotonicity of these means. We also show that these functionals are exponentially convex and give some applications of them by using the log-convexity and exponential convexity.

Recommended Citation

R. Bibi et al., "Cauchy-Type Means and Exponential and Logarithmic Convexity for Superquadratic Functions on Time Scales," Annals of Functional Analysis, vol. 6, no. 1, pp. 59 - 83, Duke University Press, Jan 2015.

The definitive version is available at https://doi.org/10.15352/afa/06-1-6

Department(s)

Mathematics and Statistics

Keywords and Phrases

Cauchy means; Jensen inequality; Superquadratic functions; Time scale

International Standard Serial Number (ISSN)

2008-8752

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2015 Duke University Press, All rights reserved.

Publication Date

01 Jan 2015