Some inequalities for interval-valued functions on time scales

• Author(s): Zhao, Dafang ; Ye, Guoju ; Liu, Wei ; Torres, Delfim F. M.
• Date: 2019
• Persistent ID: http://hdl.handle.net/10773/26294
• Origin: RIA - Repositório Institucional da Universidade de Aveiro
• Subject(s): Interval-valued functions; Time scales; Hölder’s inequality; Minkowski’s inequality; Jensen’s inequality
• Document Type: Journal article
• Language: English

Description

We introduce the interval Darboux delta integral (shortly, the IDΔ -integral) and the interval Riemann delta integral (shortly, the IR Δ -integral) for interval-valued functions on time scales. Fundamental properties of ID and IR Δ -integrals and examples are given. Finally, we prove Jensen’s, Hölder’s and Minkowski’s inequalities for the IR Δ -integral. Also, some examples are given to illustrate our theorems