Cauchy-Type Means and Exponential and Logarithmic Convexity for Superquadratic Functions on Time Scales
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.
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
Mathematics and Statistics
Keywords and Phrases
Cauchy means; Jensen inequality; Superquadratic functions; Time scale
International Standard Serial Number (ISSN)
Article - Journal
© 2015 Duke University Press, All rights reserved.
01 Jan 2015