New entropy bounds via uniformly convex functions

Sayyari, Yamin

doi:10.1016/j.chaos.2020.110360

Cited by 13 publications

(4 citation statements)

References 6 publications

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“…The most used of entropies is the Shannon entropy. There are many studies regarding the characterization and application of entropy Shannon (see, e.g., [ 1 , 2 ], etc.). We are studying a way of measuring the “disorder” of the divisors of a natural number.…”

Section: Discussionmentioning

confidence: 99%

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About the Entropy of a Natural Number and a Type of the Entropy of an Ideal

Minculete

Savin

2023

Entropy

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In this article, we find some properties of certain types of entropies of a natural number. We are studying a way of measuring the “disorder” of the divisors of a natural number. We compare two of the entropies H and H¯ defined for a natural number. An useful property of the Shannon entropy is the additivity, HS(pq)=HS(p)+HS(q), where pq denotes tensor product, so we focus on its study in the case of numbers and ideals. We mention that only one of the two entropy functions discussed in this paper satisfies additivity, whereas the other does not. In addition, regarding the entropy H of a natural number, we generalize this notion for ideals, and we find some of its properties.

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Section: Discussionmentioning

confidence: 99%

“…In [ 1 ], Sayyari gave an extension of Jensen’s discrete inequality considering the class of uniformly convex functions getting lower and upper bounds for Jensen’s inequality. He applied this results in information theory and obtained new and strong bounds for Shannon’s entropy of a probability distribution.…”

Section: Introduction and Preliminariesmentioning

confidence: 99%

About the Entropy of a Natural Number and a Type of the Entropy of an Ideal

Minculete

Savin

2023

Entropy

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“…We start this section discussing two inequalities, the first is proved by using the basic properties of uniformly convex functions as proved in [9], [8, Theorem 1] and [2]. The other inequality about uniformly convexity is derived from results in [7]. 8], it is proved that the set of Φ-uniformly convex functions f which are continuously differentiable satisfy the inequality…”

Section: Improved Jensen Functional Through φ-Uniform Convexitymentioning

confidence: 99%

Extended normalized Jensen functional related to convexity, 1-quasiconvexity and superquadracity

Abramovich¹

2018

Journal of Mathematical Inequalities

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“…The motive of this study was to extend the concept of logical entropy presented in [ 13 ] to information sources. Since estimating entropy from the information source can be difficult [ 20 ], we defined the logical metric permutation entropy of a map and used it to apply for an information source.…”

Section: Introduction and Basic Notionsmentioning

confidence: 99%

Logical Entropy of Information Sources

Sayyari

Butt

2022

Entropy

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In this paper, we present the concept of the logical entropy of order m, logical mutual information, and the logical entropy for information sources. We found upper and lower bounds for the logical entropy of a random variable by using convex functions. We show that the logical entropy of the joint distributions X1 and X2 is always less than the sum of the logical entropy of the variables X1 and X2. We define the logical Shannon entropy and logical metric permutation entropy to an information system and examine the properties of this kind of entropy. Finally, we examine the amount of the logical metric entropy and permutation logical entropy for maps.

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New entropy bounds via uniformly convex functions

Cited by 13 publications

References 6 publications

About the Entropy of a Natural Number and a Type of the Entropy of an Ideal

About the Entropy of a Natural Number and a Type of the Entropy of an Ideal

Extended normalized Jensen functional related to convexity, 1-quasiconvexity and superquadracity

Logical Entropy of Information Sources

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