n-TIMES DIFFERENTIABLE PREINVEX AND PREQUASIINVEX FUNCTIONS

Year 2019, Volume: 37 Issue: 2, 529 - 540, 01.06.2019

Huriye Kadakal

Abstract

In this manuscript, a new identity for functions defined on an open invex subset of set of real numbers is established. We present new type integral inequalities for functions whose powers of nth derivatives in absolute value are preinvex and prequasiinvex functions. This paper is a generalization of studies being done for functions whose first, second, third and fourth derivatives are preinvex and prequasiinvex. Moreover, the results we obtained in this article coincide with the previous ones in special cases.

Keywords

Invex set, preinvex function, prequasiinvex function, Hölder integral inequality, power-mean integral inequality.

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