TY - JOUR AU - Adeel, Muhammad AU - Khan, Khuram Ali AU - Pečarić, Ðilda AU - Pečarić, Josip PY - 2020 TI - Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher order convex functions via Taylor polynomial JO - Journal of Mathematics and Computer Science SP - 322--334 VL - 21 IS - 4 AB - In this paper, Levinson-type inequalities are generalized by using Taylor polynomial for the class of \(k\)-convex \((k \geq 3)\) functions. Bounds for the remainders in new generalized identities involving data points of two types are given by using Čebyšev, Grúss and Ostrowski-type inequalities. In seek of applications of our results to information theory, new generalizations based on \(f\)-divergence estimates are also proven. Moreover, some inequalities for Shannon entropies are deduced as well. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.021.04.05 DO - 10.22436/jmcs.021.04.05 ID - Adeel2020 ER - TY - JOUR TI - Generalization of the Levinson inequality with applications to information theory AU - M. Adeel AU - K. A. Khan AU - Ð. Pečarić AU - J. Pečarić JO - J. Inequal. Appl. PY - 2019 DA - 2019// VL - 2019 ID - Adeel2019 ER - TY - JOUR TI - Levinson type inequalities for higher order convex functions via Abel-Gontscharoff interpolation AU - M. Adeel AU - K. A. Khan AU - Ð. Pečarić AU - J. Pečarić JO - Adv. Difference Equ. PY - 2019 DA - 2019// VL - 2019 ID - Adeel2019 ER - TY - JOUR TI - Estimation of $f$-divergence and Shannon entropy by Levinson type inequalities via new Green's functions and Lidstone polynomial AU - M. Adeel AU - K. A. Khan AU - Ð. Pečarić AU - J. Pečarić JO - Adv. Difference Equ. 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