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In 2003, Mercer gave a variant of Jensen\u2019s inequality which is known as Jensen\u2013Mercer\u2019s inequality. The purpose of this article is to propose new bounds for Csisz\u00e1r and related divergences by means of Jensen\u2013Mercer\u2019s inequality. Also, we investigate several new bounds for Zipf\u2013Mandelbrot entropy. The idea of this article may further stimulate research on information theory with the help of Jensen\u2013Mercer\u2019s inequality.<\/jats:p>","DOI":"10.1155\/2020\/8928691","type":"journal-article","created":{"date-parts":[[2020,11,6]],"date-time":"2020-11-06T14:57:23Z","timestamp":1604674643000},"page":"1-8","source":"Crossref","is-referenced-by-count":16,"title":["New Estimates for Csisz\u00e1r Divergence and Zipf\u2013Mandelbrot Entropy via Jensen\u2013Mercer\u2019s Inequality"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5373-4663","authenticated-orcid":true,"given":"Muhammad","family":"Adil Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4826-6065","authenticated-orcid":true,"given":"Zakir","family":"Husain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0944-2134","authenticated-orcid":true,"given":"Yu-Ming","family":"Chu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Huzhou University, Huzhou 313000, China"},{"name":"Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, China"}]}],"member":"311","reference":[{"key":"1","volume-title":"Convex Functions, Partial Orderings, and Statistical Applications","author":"J. 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