We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond alpha Hölder's and Minkowski's interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results.


Mathematics and Statistics

Publication Status

Open Access

Keywords and Phrases

Diamond-alpha integral; Hölder's inequalities; Interval-valued functions; Jensen's inequalities; Minkowski's inequalities; Time scales

International Standard Serial Number (ISSN)

1029-242X; 1025-5834

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2023 The Authors, All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 Jan 2023