Multiple Diamond-Alpha Integral in General Form and Their Properties, Applications

Zhong-Xuan Mao, Ya-Ru Zhu, Jun-Ping Hou, Chun-Ping Ma and Shi-Pu Liu
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Zhong-Xuan Mao: Department of Mathematics and Physics, North China Electric Power University, Yonghua Street 619, Baoding 071003, China
Ya-Ru Zhu: Department of Mathematics and Physics, North China Electric Power University, Yonghua Street 619, Baoding 071003, China
Jun-Ping Hou: Department of Mathematics and Physics, North China Electric Power University, Yonghua Street 619, Baoding 071003, China
Chun-Ping Ma: Department of Mathematics and Physics, North China Electric Power University, Yonghua Street 619, Baoding 071003, China
Shi-Pu Liu: Department of Mathematics and Physics, North China Electric Power University, Yonghua Street 619, Baoding 071003, China

Mathematics, 2021, vol. 9, issue 10, 1-20

Abstract: In this paper, we introduce the concept of n -dimensional Diamond-Alpha integral on time scales. In particular, it transforms into multiple Delta, Nabla and mixed integrals by taking different values of alpha. Some of its properties are explored, and the relationship between it and the multiple mixed integral is provided. As an application, we establish some weighted Ostrowski type inequalities through the new integral. These new inequalities expand some known inequalities in the monographs and papers, and in addition, furnish some other interesting inequalities. Examples of Ostrowski type inequalities are posed in detail at the end of the paper.

Keywords: multiple Diamond-Alpha integral; Ostrowski type inequalities; Delta integral; Nabla integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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