Construction of a new generalization for n-polynomial convexity with their certain inequalities

Year 2024, Early Access, 1 - 13

Mahir Kadakal , İmdat İşcan , Huriye Kadakal

https://doi.org/10.15672/hujms.1310861

Cited By: 2

Abstract

In this paper, we first construct a new generalization of n-polynomial convex function. By making use of this construction, we derive certain inequalities for this new generalization and show that the first derivative in absolute value corresponds to a new class of n polynomial convexity. Also, we see that the obtained results in the paper while comparing
with Hölder, Hölder-İşcan and power-mean, improved-power-mean integral inequalities show that the results give a better approach than the others. Finally, we conclude our paper with applications containing some means.

Keywords

Convex function, generalized n-polynomial convexity, Hermite-Hadamard inequality

References

• 1] P. Agarwal, M. Kadakal, İ. İşcan and Y.M. Chu, Better approaches for n-times differentiable convex functions, Mathematics, 8 (6), 950, 2020.