New refinements of Shannon’s entropy upper bounds

Abstract

Shannon’s entropy, as metric entropy, is in general difficult to calculate and even to estimate. Tapus and Popescu (2012) and Sayyari (2020) presented the, upper bound for Shannon’s entropy and refine the recent Shannon’s entropy upper bound given by Guoxiang Lu (2018). In this paper, we obtain a better upper bound for Shannon’s entropy.

Subject Classification:

• 37B40
• 26B25
• 94A17
• 26D15
• 26D20

Keywords:

• Shannon’s entropy
• Jensen’s inequality
• Uniformly convex function
• Bounds
• Refinements