TY - JOUR AU - S. I. Butt AU - Ð. Pečarić AU - J. Pečarić PY - 2023/01/17 Y2 - 2024/03/29 TI - Several Jensen–Grüss inequalities with applications in information theory JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 74 IS - 12 SE - Research articles DO - 10.37863/umzh.v74i12.6554 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6554 AB - UDC 517.5Several integral Jensen–Grüss  inequalities are proved together with their refinements.  Some new bounds for integral Jensen–Chebyshev  inequality are obtained. The multidimensional integral variants are also presented.  In addition, some integral Jensen–Grüss  inequalities for monotone  and completely monotone functions are established.  Finally, as an application, we present the refinements  for Shannon's entropy. ER -