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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.
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Details
1 Kırklareli University, Department of Mathematics, Faculty of Arts and Sciences, Kırklareli, Turkey (GRID:grid.448786.1) (ISNI:0000 0004 0399 5728)
2 Bayburt University, Department of Customs Management, Faculty of Applied Sciences, Bayburt, Turkey (GRID:grid.440426.0) (ISNI:0000 0004 0399 2906)
3 Giresun University, Department of Mathematics, Faculty of Arts and Sciences, Giresun, Turkey (GRID:grid.411709.a) (ISNI:0000 0004 0399 3319)
4 Bayburt University, Department of Primary Education, Faculty of Education, Bayburt, Turkey (GRID:grid.440426.0) (ISNI:0000 0004 0399 2906)