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- Title
Improving Jensen-type Inequalities Via the Sum of the Lidstone Polynomials.
- Authors
Krnić, Mario
- Abstract
We aim to establish refinements of the Jensen inequality for the classes of completely convex and absolutely convex functions. In the first case the refinement is expressed in terms of the alternating sum of Lidstone polynomials, while in the second case we deal with the sum of the Lidstone polynomials. As an application, more accurate power mean inequalities are derived. In particular, we obtain strengthened versions of arithmetic–geometric mean inequality in a difference and a quotient form. Finally, we also establish more accurate form of the Hölder inequality.
- Subjects
JENSEN'S inequality; POLYNOMIALS; CONVEX functions
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2024, Vol 47, Issue 3, p1
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-024-01670-y