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Chebyshev–Jensen-Type Inequalities Involving χ -Products and Their Applications in Probability Theory

Author

Listed:
  • Ru Liu

    (College of Computer Science, Chengdu University, Chengdu 610106, China)

  • Jiajin Wen

    (College of Computer Science, Chengdu University, Chengdu 610106, China)

  • Lingzhi Zhao

    (School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, China)

Abstract

By means of the functional analysis theory, reorder method, mathematical induction and the dimension reduction method, the Chebyshev-Jensen-type inequalities involving the χ -products ⟨ · ⟩ χ and [ · ] χ are established, and we proved that our main results are the generalizations of the classical Chebyshev inequalities. As applications in probability theory, the discrete with continuous probability inequalities are obtained.

Suggested Citation

  • Ru Liu & Jiajin Wen & Lingzhi Zhao, 2024. "Chebyshev–Jensen-Type Inequalities Involving χ -Products and Their Applications in Probability Theory," Mathematics, MDPI, vol. 12(10), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1495-:d:1392281
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