Refinement of Jensen’s inequality and estimation of f- and Rényi divergence via Montgomery identity [PDF]
Journal of Inequalities and Applications, 2018 Jensen’s inequality is important for obtaining inequalities for divergence between probability distribution. By applying a refinement of Jensen’s inequality (Horváth et al. in Math. Inequal. Appl.
Khuram Ali Khan +3 more
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Bivariate Montgomery identity for alpha diamond integrals [PDF]
Advances in Difference Equations, 2019 In the paper, some variants of Montgomery identity with the help of delta and nabla integrals are established which are useful to produce Montgomery identity involving alpha diamond integrals for function of two variables.
Masud Ahmad +4 more
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Generalizations of Steffensen’s inequality via the extension of Montgomery identity
Open Mathematics, 2018 In this paper, we obtained new generalizations of Steffensen’s inequality for n-convex functions by using extension of Montgomery identity via Taylor’s formula. Since 1-convex functions are nondecreasing functions, new inequalities generalize Stefensen’s
Aljinović Andrea Aglić +2 more
doaj +7 more sources
On Ostrowski Type Inequalities via the Extended Version of Montgomery’s Identity
Mathematics, 2022 In this paper, we obtain new Ostrowski type inequalities by using the extended version of Montgomery identity and Green’s functions. We also give estimations of the difference between two integral means.
Asif R. Khan +2 more
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Generalizations of Hardy-Type Inequalities by Montgomery Identity and New Green Functions
Axioms, 2023 In this paper we extend general Hardy’s inequality by appropriately combining Montgomery’s identity and Green functions. Related Grüss and Ostrowski-type inequalities are also derived.
Kristina Krulić Himmelreich +3 more
doaj +5 more sources
Uniform Treatment of Jensen’s Inequality by Montgomery Identity [PDF]
Journal of Mathematics, 2021 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.
Tahir Rasheed +4 more
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Generalized Steffensen’s inequality by Montgomery identity [PDF]
Journal of Inequalities and Applications, 2019 By using generalized Montgomery identity and Green functions we proved several identities which assist in developing connections with Steffensen’s inequality.
Saad Ihsan Butt +3 more
doaj +4 more sources
The extension of Montgomery identity via Fink identity with applications [PDF]
Journal of Inequalities and Applications, 2005 The new extension of the weighted Montgomery identity is given by using Fink identity and is used to obtain some Ostrowski-type inequalities and estimations of the difference of two integral means.
PečArić J +2 more
doaj +5 more sources
New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity [PDF]
Journal of Inequalities and Applications, 2017 The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green’s functions.
Nasir Mehmood +3 more
doaj +2 more sources
Jensen-Type Inequalities, Montgomery Identity and Higher-Order Convexity [PDF]
Mediterranean Journal of Mathematics, 2022 Motivated by some recent results known from the literature, in this paper we establish a class of Jensen-type inequalities referring to functions of an even degree of convexity. The main idea of proving our results is a transformation of the classical Jensen functional via the Montgomery identity which is suitable to study in companion with the higher ...
Mario Krnić
exaly +4 more sources