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1. Generalized k-fractional integral inequalities associated with (α,m)-convex functions.

Author

Kang, S. M., Farid, G., Waseem, M., Ullah, S., Nazeer, W., and Mehmood, S.

Subjects
GENERALIZED integrals, INTEGRAL inequalities, FRACTIONAL integrals, CONVEX functions, MATHEMATICS
Abstract

This research investigates bounds of the sum of left-sided and right-sided fractional integrals in a compact form. These bounds are established by using (α , m) -convex functions. The results of this paper also have connection with some known and already published results (Dragomir and Agarwal in Appl. Math. Lett. 11(5):91–95, 1998; Farid in J. Anal. 2018, https://doi.org/10.1007/s41478-0079-4; Farid et al. in Mathematics 2018(6):248, 2018). Moreover, the investigated results are applied to the end points as well as the mid point of the domain and some interesting consequences have been obtained. [ABSTRACT FROM AUTHOR]

Published
2019
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2. A new refinement of Jensen’s inequality with applications in information theory

Author

Xiao Lei and Lu Guoxiang

Subjects
refinements, jensen’s inequality, information theory, shannon’s entropy, f-divergences, bounds, 26b25, 26d15, 94a17, Mathematics, QA1-939
Abstract

In this paper, we present a new refinement of Jensen’s inequality with applications in information theory. The refinement of Jensen’s inequality is obtained based on the general functional in the work of Popescu et al. As the applications in information theory, we provide new tighter bounds for Shannon’s entropy and some f-divergences.

Published
2020
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3. A new refinement of Jensen’s inequality with applications in information theory

Author

Guoxiang Lu and Lei Xiao

Subjects
refinements, General Mathematics, lcsh:Mathematics, 010102 general mathematics, 94a17, 010103 numerical & computational mathematics, Information theory, lcsh:QA1-939, 01 natural sciences, GeneralLiterature_MISCELLANEOUS, 26b25, shannon’s entropy, 26d15, jensen’s inequality, 0101 mathematics, bounds, Mathematical economics, Jensen's inequality, Mathematics, information theory, f-divergences
Abstract

In this paper, we present a new refinement of Jensen’s inequality with applications in information theory. The refinement of Jensen’s inequality is obtained based on the general functional in the work of Popescu et al. As the applications in information theory, we provide new tighter bounds for Shannon’s entropy and some f-divergences.

Published
2020