Some Inequalities for <img src=image/13426606_01.gif>-times Differentiable Strongly Convex Functions

Abstract

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 <img src=image/13426606_01.gif>-times. This study deals with some general identities introduced for <img src=image/13426606_01.gif>-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 <img src=image/13426606_01.gif>^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.