Generalized Jensen’s functional on time scales via extended Montgomery identity

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. Moreover, the bounds have been suggested for identities associated with the generalized Jensen-type functional.

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Bibliographic Details
Published in:	Journal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 17
Main Authors:	Ramzan, Sofia, Nosheen, Ammara, Bibi, Rabia, Pečarić, Josip
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 05-06-2021 Springer Nature B.V SpringerOpen
Subjects:	Analysis Applications of Mathematics Convex functions Diamond integrals Diamonds Identities Jensen’s inequality Mathematics Mathematics and Statistics Time scales calculus Jensen’s inequality Convex functions Time scales calculus Diamond integrals
Online Access:	Get full text
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Description
Summary:	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. Moreover, the bounds have been suggested for identities associated with the generalized Jensen-type functional.
ISSN:	1029-242X 1025-5834 1029-242X
DOI:	10.1186/s13660-021-02629-4