Inequalities for interval-valued Riemann diamond-alpha integrals

被引：1

作者：

Bohner, Martin ^{[1
]}

Nguyen, Linh ^{[2
]}

Schneider, Baruch ^{[3
]}

Truong, Tri ^{[3
]}

机构：

[1] Missouri S&T, Rolla, MO 65409 USA

[2] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

[3] Univ Ostrava, Fac Sci, Dept Math, Ostrava 70103, Czech Republic

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2023年 / 2023卷 / 01期

关键词：

Interval-valued functions; Time scales; Diamond-alpha integral; Jensen's inequalities; Holder's inequalities; Minkowski's inequalities; OPIAL-TYPE INEQUALITIES; TIME SCALES; HUKUHARA DIFFERENTIABILITY; OPTIMIZATION; DERIVATIVES; EQUATIONS;

D O I：

10.1186/s13660-023-02993-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Holder's and Minkowski's interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results.

引用

页数：30

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