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Generalized cyclic Jensen and information inequalities

Author

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  • Rasheed, T.
  • Butt, S.I.
  • Pečarić, Đ.
  • Pečarić, J.

Abstract

We present Levinson’s type generalizations of cyclic refinements of Jensen’s inequality by employing recent class of functions that further characterize and extend the family of 3-convex functions. We get monotonic cyclic Jensen’s inequalities and particularly the renowned Jensen’s inequality for 3-convex functions at a point (f∈κ1c(I)). As an applications in information theory, we first introduce new Csiszár type cyclic divergence functional for 3-convex functions and establish cyclic-Kullback–Leibler and Hellinger distances. We give monotonicity of cyclic divergence functionals which enable us to construct monotonic Shannon, Relative and Zipf–Mandelbrot entropies.

Suggested Citation

  • Rasheed, T. & Butt, S.I. & Pečarić, Đ. & Pečarić, J., 2022. "Generalized cyclic Jensen and information inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007895
    DOI: 10.1016/j.chaos.2022.112602
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    References listed on IDEAS

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    1. Sayyari, Yamin, 2020. "New entropy bounds via uniformly convex functions," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
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    Cited by:

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    2. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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