Generalized strongly n-polynomial convex functions and related inequalities release_tars4if3enbgbgm33aapbsipxm

by Serap Özcan, Mahir Kadakal, İmdat İşcan, Huriye Kadakal

Published in Boundary Value Problems by Springer Science and Business Media LLC.

2024   Volume 2024, Issue 1

Abstract

<jats:title>Abstract</jats:title>This paper focuses on introducing and examining the class of generalized strongly <jats:italic>n</jats:italic>-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly <jats:italic>n</jats:italic>-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions using the Hölder–İşcan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided.
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