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Giaccardi Inequality for s‐Convex Functions in the Second Sense for Isotonic Linear Functionals and Associated Results

Author

Listed:
  • Dong Chen
  • Dina Abuzaid
  • Atiq Ur Rehman
  • Aqsa Rani

Abstract

In this paper, a well‐known inequality called Giaccardi inequality is established for isotonic linear functionals by applying s‐convexity in the second sense, which leads to notable Petrović inequality. As a special case, discrete and integral versions of Giaccardi inequality are derived along with the Petrović inequality as a particular case. In application point of view, newly established inequalities are derived for different time scales.

Suggested Citation

  • Dong Chen & Dina Abuzaid & Atiq Ur Rehman & Aqsa Rani, 2022. "Giaccardi Inequality for s‐Convex Functions in the Second Sense for Isotonic Linear Functionals and Associated Results," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4145336
    DOI: 10.1155/2022/4145336
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    References listed on IDEAS

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    1. Matloob Anwar & Rabia Bibi & Martin Bohner & Josip Pečarić, 2011. "Integral Inequalities on Time Scales via the Theory of Isotonic Linear Functionals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. Jiang Zhu & Ling Wu, 2015. "Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-23, April.
    3. Matloob Anwar & Rabia Bibi & Martin Bohner & Josip Pečarić, 2011. "Integral Inequalities on Time Scales via the Theory of Isotonic Linear Functionals," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-16, July.
    4. Jiang Zhu & Ling Wu, 2015. "Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
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