Generalized cyclic Jensen and information inequalities

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

Chaos, Solitons & Fractals, 2022, vol. 163, issue C

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.

Keywords: 3-convex function; Entropy; Cyclic-divergence functional; Cyclic-Kullback–Leibler distance (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007895

DOI: 10.1016/j.chaos.2022.112602

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