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Superquadratic function and its applications in information theory via interval calculus

Author

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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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