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.
M. Bohner et al., "Inequalities For Interval-valued Riemann Diamond-alpha Integrals," Journal of Inequalities and Applications, vol. 2023, no. 1, article no. 86, SpringerOpen, Jan 2023.
The definitive version is available at https://doi.org/10.1186/s13660-023-02993-3
Mathematics and Statistics
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)
Article - Journal
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01 Jan 2023