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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zhong-Xuan Mao & Ya-Ru Zhu & Jun-Ping Hou & Chun-Ping Ma & Shi-Pu Liu, 2021. "Multiple Diamond-Alpha Integral in General Form and Their Properties, Applications," Mathematics, MDPI, vol. 9(10), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1123-:d:555473
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    References listed on IDEAS

    as
    1. Zhong-Xuan Mao & Ya-Ru Zhu & Bao-Hua Guo & Fu-Hai Wang & Yu-Hua Yang & Hai-Qing Zhao, 2021. "Qi Type Diamond-Alpha Integral Inequalities," Mathematics, MDPI, vol. 9(4), pages 1-24, February.
    2. Liu, Wenjun & Tuna, Adnan, 2015. "Diamond-α weighted Ostrowski type and Grüss type inequalities on time scales," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 251-260.
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