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A new class of convex functions and applications in entropy and analysis

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  • Sayyari, Yamin
  • Dehghanian, Mehdi

Abstract

In this article, we introduce the concepts of k-harmonic mean and k-harmonically convex functions. As an application of k-harmonic mean, we present a model in physics. Also, we prove Jensen type, Hermite–Hadamard type and Mercer type inequalities for these functions. Further, using this results, we give new bounds for Shannon entropy and geometrically mean.

Suggested Citation

  • Sayyari, Yamin & Dehghanian, Mehdi, 2024. "A new class of convex functions and applications in entropy and analysis," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924002297
    DOI: 10.1016/j.chaos.2024.114677
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    References listed on IDEAS

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    1. 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).
    2. Sayyari, Yamin, 2020. "New entropy bounds via uniformly convex functions," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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