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Superquadratic function and its applications in information theory via interval calculus

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  • Butt, Saad Ihsan
  • Khan, Dawood

Abstract

The goal of this study is to introduce a new class of superquadraticity, which is known as superquadratic interval valued function (superquadratic I-V-F) and establish its properties via order relations of intervals. By utilizing the definitions and properties of superquadratic I-V-F, we come up with new integral inequalities such that Jensen’s, converse Jensen’s, Mercer Jensen’s and Hermite–Hadamard types. In addition to this, we provide a fractional version of Hermite–Hadamard’s type inequalities for superquadratic I-V-Fs. The findings are validated by specific numerical computations and graphical illustrations that include a certain number of relevant examples. We also offer the applications of the established results in information theory such that we determine the novel estimates for Shannon’s and relative entropies.

Suggested Citation

  • Butt, Saad Ihsan & Khan, Dawood, 2025. "Superquadratic function and its applications in information theory via interval calculus," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:chsofr:v:190:y:2025:i:c:s0960077924013006
    DOI: 10.1016/j.chaos.2024.115748
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    References listed on IDEAS

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    1. Khan, Muhammad Bilal & Othman, Hakeem A. & Santos-García, Gustavo & Saeed, Tareq & Soliman, Mohamed S., 2023. "On fuzzy fractional integral operators having exponential kernels and related certain inequalities for exponential trigonometric convex fuzzy-number valued mappings," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Butt, Saad Ihsan & Yousaf, Saba & Akdemir, Ahmet Ocak & Dokuyucu, Mustafa Ali, 2021. "New Hadamard-type integral inequalities via a general form of fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    4. Guangzhou Li & Feixiang Chen, 2014. "Hermite‐Hadamard Type Inequalities for Superquadratic Functions via Fractional Integrals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Khan, Muhammad Bilal & Santos-García, Gustavo & Noor, Muhammad Aslam & Soliman, Mohamed S., 2022. "Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Guangzhou Li & Feixiang Chen, 2014. "Hermite-Hadamard Type Inequalities for Superquadratic Functions via Fractional Integrals," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, August.
    7. Du, Tingsong & Zhou, Taichun, 2022. "On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    8. Khan, Dawood & Butt, Saad Ihsan, 2024. "Superquadraticity and its fractional perspective via center-radius cr-order relation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. Rasheed, T. & Butt, S.I. & Pečarić, Đ. & Pečarić, J., 2022. "Generalized cyclic Jensen and information inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    10. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
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