Abstract

This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-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.

Details

Title
Generalized strongly n-polynomial convex functions and related inequalities
Author
Özcan, Serap 1 ; Kadakal, Mahir 2 ; İşcan, İmdat 3 ; Kadakal, Huriye 4 

 Kırklareli University, Department of Mathematics, Faculty of Arts and Sciences, Kırklareli, Turkey (GRID:grid.448786.1) (ISNI:0000 0004 0399 5728) 
 Bayburt University, Department of Customs Management, Faculty of Applied Sciences, Bayburt, Turkey (GRID:grid.440426.0) (ISNI:0000 0004 0399 2906) 
 Giresun University, Department of Mathematics, Faculty of Arts and Sciences, Giresun, Turkey (GRID:grid.411709.a) (ISNI:0000 0004 0399 3319) 
 Bayburt University, Department of Primary Education, Faculty of Education, Bayburt, Turkey (GRID:grid.440426.0) (ISNI:0000 0004 0399 2906) 
Pages
32
Publication year
2024
Publication date
Dec 2024
Publisher
Hindawi Limited
ISSN
16872762
e-ISSN
16872770
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2931870612
Copyright
© The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.