Generalizations of Shannon type inequalities via diamond integrals on time scales

Abstract

Abstract The paper generalizes Shannon-type inequalities for diamond integrals. It includes two-dimensional Hölder’s inequality and Cauchy–Schwartz’s inequality, which help to prove weighted Grüss’s inequality for diamond integrals. Jensen’s inequality and Grüss’s inequality are used to provide Shannon-type inequalities for diamond integrals. Shannon-type inequalities for multiple integrals are also part of the discussion. Moreover, many distributions are deduced from the main results, and new bounds are obtained.

Keywords

• Shannon entropy
• Diamond integral
• Information theory