<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>In this study, some new inequalities for <italic>n</italic>-times differentiable strongly <italic>s</italic>-convex functions are introduced. These inequalities are obtained via the perturbed trapezoid inequality. We obtain a better bound for the mentioned inequalities with the strongly <italic>s</italic>-convex functions. <italic>nth </italic>derivatives of absolute values of the handled functions are strongly <italic>s</italic>-convex. Finally, the theorems presented for strongly <italic>s</italic>-convex functions are reduced to the ones given for <italic>s</italic>-convex functions when the constant from strongly <italic>s</italic>-convexity vanishes.</p>
</abstract>

In this study, some new inequalities for n-times differentiable strongly s-convex functions are introduced. These inequalities are obtained via the perturbed trapezoid inequality. We obtain a better bound for the mentioned inequalities with the strongly s-convex functions. nth derivatives of absolute values of the handled functions are strongly s-convex. Finally, the theorems presented for strongly s-convex functions are reduced to the ones given for s-convex functions when the constant from strongly s-convexity vanishes.

On <italic>n</italic>-times differentiable strongly <italic>s</italic>-convex functions

Manisa Celal Bayar University, Faculty of Science and Letters

İstanbul Nişantaşı University, Faculty of Economics, Administrative and Social Sciences

Department of Management Information Systems

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

On -times differentiable strongly -convex functions

In this study, some new inequalities for n-times differentiable strongly s-convex functions are introduced. These inequalities are obtained via the perturbed...

On n-times differentiable strongly s-convex functions

Published Online: Sep 13, 2023

Page range: 201 - 210

Received: Jun 07, 2023

Accepted: Aug 11, 2023

DOI: https://doi.org/10.2478/ijmce-2023-0016

Keywords
-convex function, strongly -convex function, perturbed trapezoid inequalities

© 2023 Duygu Dönmez Demir et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On n-times differentiable strongly s-convex functions

Published Online: Sep 13, 2023

Page range: 201 - 210

Received: Jun 07, 2023

Accepted: Aug 11, 2023

DOI: https://doi.org/10.2478/ijmce-2023-0016

Keywords-convex function, strongly -convex function, perturbed trapezoid inequalities

© 2023 Duygu Dönmez Demir et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
-convex function, strongly -convex function, perturbed trapezoid inequalities