Generalized cyclic Jensen and information inequalities. (October 2022)

• Record Type: Journal Article
• Authors: Rasheed, T.; Butt, S.I.; Pečarić, Đ.; Pečarić, J.
• Is Part Of: Chaos, solitons and fractals. Volume 163(2022)
• Publication Date: 2022-10
• Subjects: primary 26A51 26D15 26E60 94A17 94A15; 3-convex function -- Entropy -- Cyclic-divergence functional -- Cyclic-Kullback–Leibler distance; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112602
• Languages: English
• ISSNs: 0960-0779

Abstract

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 ∈ κ 1 c ( 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. Highlights: We present Levinson's type generalizations of cyclic refinements of Jensen's inequality by using the recent generalized class of convex functions. We obtain monotonic cyclic Jensen's inequalities for 3-convex function at a point. We introduce new Csiszar 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.