Montgomery identity and Ostrowski-type inequalities via quantum calculus [PDF]
Open Mathematics, 2021 In this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus.
Thanin Sitthiwirattham +2 more
exaly +6 more sources
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
Andrea Aglic Aljinovic +2 more
exaly +9 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
doaj +5 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 +6 more sources
Generalized Jensen’s functional on time scales via extended Montgomery identity [PDF]
Journal of Inequalities and Applications, 2021 In the paper, we use Jensen’s inequality for diamond integrals and generalize it for n-convex functions with the help of an extended Montgomery identity.
Sofia Ramzan +3 more
doaj +4 more sources
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 +5 more sources
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
doaj +4 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 +4 more sources
Generalization of Montgomery identity via Taylor formula on time scales [PDF]
Journal of Inequalities and Applications, 2022 In the current paper, a generalized Montgomery identity is obtained with the help of Taylor’s formula on time scales. The obtained identity is used to establish Ostrowski inequality, mid-point inequality, and trapezoid inequality.
Khuram Ali Khan +2 more
exaly +3 more sources
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.
Khalid Mahmood Awan +2 more
exaly +4 more sources