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- Title
Inequalities for interval-valued Riemann diamond-alpha integrals.
- Authors
Bohner, Martin; Nguyen, Linh; Schneider, Baruch; Truong, Tri
- Abstract
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.
- Subjects
RIEMANN integral; JENSEN'S inequality; CONCAVE functions; INTEGRAL inequalities; FUZZY sets
- Publication
Journal of Inequalities & Applications, 2023, Vol 2023, Issue 1, p1
- ISSN
1025-5834
- Publication type
Article
- DOI
10.1186/s13660-023-02993-3