scholarly journals Extensions and improvements of Sherman’s and related inequalities for n-convex functions

2017 ◽  
Vol 15 (1) ◽  
pp. 936-947
Author(s):  
Slavica Ivelić Bradanović ◽  
Josip Pečarić
Keyword(s):  
Convex Functions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Arithmetic Means ◽  
Fink’S Identity ◽  
New Inequalities

AbstractThis paper gives extensions and improvements of Sherman’s inequality forn-convex functions obtained by using new identities which involve Green’s functions and Fink’s identity. Moreover, extensions and improvements of Majorization inequality as well as Jensen’s inequality are obtained as direct consequences. New inequalities between geometric, logarithmic and arithmetic means are also established.

scholarly journals Bounds for the normalised Jensen functional

2006 ◽  
Vol 74 (3) ◽  
pp. 471-478 ◽  
Author(s):  
Sever S. Dragomir
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Normed Spaces ◽  
Jensen's Inequality ◽  
Linear Spaces ◽  
Leibler Divergence ◽  
Jensen Functional ◽  
New Inequalities

New inequalities for the general case of convex functions defined on linear spaces which improve the famous Jensen's inequality are established. Particular instances in the case of normed spaces and for complex and real n-tuples are given. Refinements of Shannon's inequality and the positivity of Kullback-Leibler divergence are obtained.

scholarly journals Refinements of some Hardy–Littlewood–Pólya type inequalities via Green’s functions and Fink’s identity and related results

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sadia Khalid ◽  
Josip Pečarić
Keyword(s):  
Shannon Entropy ◽  
Convex Functions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Čebyšev Functional ◽  
Grüss Type Inequalities ◽  
Fink’S Identity

AbstractIn this paper, first we present some interesting identities associated with Green’s functions and Fink’s identity, and further we present some interesting inequalities for r-convex functions. We also present refinements of some Hardy–Littlewood–Pólya type inequalities and give an application to the Shannon entropy. Furthermore, we use the Čebyšev functional and Grüss type inequalities and present the bounds for the remainder in the obtained identities. Finally, we use the obtained identities together with Hölder’s inequality for integrals and present Ostrowski type inequalities.

scholarly journals Generalizations of the Jensen–Mercer Inequality via Fink’s Identity

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2406
Author(s):  
Anita Matković
Keyword(s):  
Convex Functions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Linear Functionals ◽  
Definition Of ◽  
Fink’S Identity

We generalize an integral Jensen–Mercer inequality to the class of n-convex functions using Fink’s identity and Green’s functions. We study the monotonicity of some linear functionals constructed from the obtained inequalities using the definition of n-convex functions at a point.

On Some Integral Inequalities Related to Hardy's

1977 ◽  
Vol 20 (3) ◽  
pp. 307-312 ◽  
Author(s):  
Christopher Olutunde Imoru
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Integral Inequalities ◽  
Hardy’S Inequality ◽  
Jensen's Inequality ◽  
Hardy's Inequality ◽  
Special Case

AbstractWe obtain mainly by using Jensen's inequality for convex functions an integral inequality, which contains as a special case Shun's generalization of Hardy's inequality.

scholarly journals INEQUALITIES IN TERMS OF THE GÂTEAUX DERIVATIVES FOR CONVEX FUNCTIONS ON LINEAR SPACES WITH APPLICATIONS

2011 ◽  
Vol 83 (3) ◽  
pp. 500-517 ◽  
Author(s):  
S. S. DRAGOMIR
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Linear Spaces ◽  
Divergence Measures ◽  
Gateaux Derivatives ◽  
Gâteaux Derivatives

AbstractSome inequalities in terms of the Gâteaux derivatives related to Jensen’s inequality for convex functions defined on linear spaces are given. Applications for norms, mean f-deviations and f-divergence measures are provided as well.

scholarly journals Generalized Jensen-Mercer Inequality for Functions with Nondecreasing Increments

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Asif R. Khan ◽  
Sumayyah Saadi
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Higher Dimensions ◽  
Jensen's Inequality ◽  
Valuable Addition ◽  
Interesting Variation ◽  
Integral Version ◽  
The Way

In the year 2003, McD Mercer established an interesting variation of Jensen’s inequality and later in 2009 Mercer’s result was generalized to higher dimensions by M. Niezgoda. Recently, Asif et al. has stated an integral version of Niezgoda’s result for convex functions. We further generalize Niezgoda’s integral result for functions with nondecreasing increments and give some refinements with applications. In the way, we generalize an important result, Jensen-Boas inequality, using functions with nondecreasing increments. These results would constitute a valuable addition to Jensen-type inequalities in the literature.

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