Generalizations of cyclic refinements of Jensen's inequality by Lidstone's polynomial with applications in information theory

Abstract

Jensen's inequality plays pivotal role in attaining divergence between probability distributions. Shannon, Relative and Zipf-Mandelbrot entropies have ample applications in many applied sciences, especially in information theory, biology, economics, etc. In the present paper, we have obtained new generalizations of cyclic refinements of Jensen's inequality using different new Green functions by employing Lidstone's polynomial. As an application of our obtained results we have given new entropic bounds. Also, we have established the connections between Shannon and Relative entropy with Zipf-Mandelbrot entropy. (2010): 26A51, 26D15, 26E60, 94A17, 94A15. Mathematics subject classification

Fractional Hermite–Jensen–Mercer Integral Inequalities with respect to Another Function and Application

“…Furthermore, this inequality has been used in various areas of sciences and technology to solve several problems, such as engineering, mathematical statistics, financial economics, and computer science. Some recent results can be seen in [12][13][14].…”

New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function

“…Jensen's inequality is the key to success in extracting applications in information theory. It is effective in finding estimates for several quantitative measures in information theory about continuous random variables, see [1][2][3]. The (J-I) can be stated as a generalization of convex functions as follows:…”

n–polynomial exponential type p–convex function with some related inequalities and their applications

“…It is also known as classical equation of (H–H) inequality. The Hermite–Hadamard inequality asserts that, if a function is convex in I for and , then Interested readers can refer to [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] .…”

“…Eventually the theory of inequalities may be regarded as an independent area of mathematics. For the applications of inequalities interested readers refer to [1,2,3,4,5,6]. In recent years, a wide class of integral inequalities is being derived via different concepts of convexity.…”

“…It is also known as classical equation of (H-H) inequality. The Hermite-Hadamard inequality asserts that, if a function ∶ ⊂ ℜ → ℜ is convex in for 1 , 2 ∈ and 1 < 2 , then Interested readers can refer to [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28].…”