scholarly journals Refinement of the Jensen integral inequality

2016 ◽  
Vol 14 (1) ◽  
pp. 221-228 ◽  
Author(s):  
Silvestru Sever Dragomir ◽  
Muhammad Adil Khan ◽  
Addisalem Abathun
Keyword(s):  
Information Theory ◽  
Integral Inequality ◽  
Linear Functionals ◽  
Jensen Integral Inequality

AbstractIn this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.

scholarly journals Reverses Hardy-type inequalities via Jensen integral inequality

2021 ◽  
Vol 52 ◽  
pp. 43-51
Author(s):  
Bouharket Benaissa ◽  
Aissa Benguessoum
Keyword(s):  
Weight Function ◽  
Integral Inequality ◽  
Hölder Inequality ◽  
Integral Inequalities ◽  
Hardy Inequalities ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Jensen Integral Inequality ◽  
Number Of Authors

The integral inequalities concerning the inverse Hardy inequalities have been studied by a large number of authors during this century, of these articles have appeared, the work of Sulaiman in 2012, followed by Banyat Sroysang who gave an extension to these inequalities in 2013. In 2020 B. Benaissa presented a generalization of inverse Hardy inequalities. In this article, we establish a new generalization of these inequalities by introducing a weight function and a second parameter. The results will be proved using the Hölder inequality and the Jensen integral inequality. Several the reverses weighted Hardy’s type inequalities and the reverses Hardy’s type inequalities were derived from the main results.

scholarly journals Uniform Treatment of Jensen’s Inequality by Montgomery Identity

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Tahir Rasheed ◽  
Saad Ihsan Butt ◽  
Đilda Pečarić ◽  
Josip Pečarić ◽  
Ahmet Ocak Akdemir
Keyword(s):  
Information Theory ◽  
Integral Inequality ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Fractional Integrals ◽  
Jensen's Inequality ◽  
Hadamard Inequality ◽  
Montgomery Identity ◽  
Discrete Inequality ◽  
Uniform Treatment

We generalize Jensen’s integral inequality for real Stieltjes measure by using Montgomery identity under the effect of n − convex functions; also, we give different versions of Jensen’s discrete inequality along with its converses for real weights. As an application, we give generalized variants of Hermite–Hadamard inequality. Montgomery identity has a great importance as many inequalities can be obtained from Montgomery identity in q − calculus and fractional integrals. Also, we give applications in information theory for our obtained results, especially for Zipf and Hybrid Zipf–Mandelbrot entropies.

scholarly journals One Concave-Convex Inequality and Its Consequences

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1639
Author(s):  
Julije Jakšetić
Keyword(s):  
Integral Inequality ◽  
Linear Functionals ◽  
Monotone Functions ◽  
Completely Monotone Functions ◽  
Convex Inequality ◽  
Completely Monotone ◽  
Starting Point ◽  
Increasing Functions

Our starting point is an integral inequality that involves convex, concave and monotonically increasing functions. We provide some interpretations of the inequality, in terms of both probability and terms of linear functionals, from which we further generate completely monotone functions and means. The latter application is seen from the perspective of monotonicity and convexity.

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