Mathematics and Statistics Vol. 10(2), pp. 390 - 396
DOI: 10.13189/ms.2022.100214
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Some Inequalities for -times Differentiable Strongly Convex Functions

Duygu Dönmez Demir *, Gülsüm Şanal
Department of Mathematics, Faculty of Art& Sciences, Manisa Celal Bayar University, 45140, Manisa, Turkey


The theory of inequality is in a process of continuous development and has become a quite effective and powerful tool in various branches of mathematics to solve many problems. Convex functions are closely related to the theory of inequality, and many important inequalities are the results of the applications of convex functions. Recently, the results obtained for convex functions have been tried to be extended for strongly convex functions. In our previous studies, the perturbed trapezoid inequality obtained for convex functions has been extended to the functions that can be differentiated -times. This study deals with some general identities introduced for -times differentiable strongly convex functions. Besides, new inequalities related to general perturbed trapezoid inequality are constructed. These inequalities are obtained for the classes of functions which th derivatives of absolute values of the mentioned functions are strongly convex. It is seen that new classes of strongly convex functions turn into those obtained for convex functions under certain conditions. Considering the upper bounds obtained for strongly convex functions, it is concluded that it is better than those obtained for convex functions.

Convex Functions, Strongly Convex Functions, Perturbed Trapezoid Inequalities

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Duygu Dönmez Demir , Gülsüm Şanal , "Some Inequalities for -times Differentiable Strongly Convex Functions," Mathematics and Statistics, Vol. 10, No. 2, pp. 390 - 396, 2022. DOI: 10.13189/ms.2022.100214.

(b). APA Format:
Duygu Dönmez Demir , Gülsüm Şanal (2022). Some Inequalities for -times Differentiable Strongly Convex Functions. Mathematics and Statistics, 10(2), 390 - 396. DOI: 10.13189/ms.2022.100214.