Weighted averages of n-convex functions via extension of Montgomery’s identity
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DOI: 10.1007/s40065-019-0245-9
Abstract: Using an extension of Montgomery’s identity and the Green’s function, we obtain new identities and related inequalities for weighted averages of n-convex functions, i.e. the sum $$\sum _{i=1}^m \rho _i h(\lambda _i)$$∑i=1mρih(λi) and the integral… read more here.
Keywords: montgomery identity; weighted averages; averages convex; convex functions ... See more keywords
New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity
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DOI: 10.1186/s13660-017-1379-y
Abstract: 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. New generalizations of an improved Popoviciu inequality are obtained by… read more here.
Keywords: new green; generalizations popoviciu; montgomery identity; new generalizations ... See more keywords
Bivariate Montgomery identity for alpha diamond integrals
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DOI: 10.1186/s13662-019-2254-6
Abstract: 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. The… read more here.
Keywords: diamond integrals; identity; alpha diamond; montgomery identity ... See more keywords
Levinson-type inequalities via new Green functions and Montgomery identity
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DOI: 10.1515/math-2020-0163
Abstract: Abstract In this study, Levinson-type inequalities are generalized by using new Green functions and Montgomery identity for the class of k-convex functions (k ≥ 3). Čebyšev-, Grüss- and Ostrowski-type new bounds are found for the… read more here.
Keywords: levinson type; new green; montgomery identity; functions montgomery ... See more keywords
Generalizations of Hardy-Type Inequalities by Montgomery Identity and New Green Functions
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DOI: 10.3390/axioms12050434
Abstract: 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. read more here.
Keywords: green functions; hardy type; type inequalities; generalizations hardy ... See more keywords