Improvements on some inequalities of Hermite Hadamard inequalities for functions when a power of the absolute value of the second derivative h and P-convex

In this paper, firstly we obtain some improvements of Hermite-Hadamard integral inequalities via h and P-convex by using Hölder-İşcan inequality. Secondly new results are established. Thirdly, we determine some new inequalities for functions when a power of the absolute value of second derivatives are h and P-convex. Finally they are compared with the old ones.Publisher's Versio

Hermite-Hadamard type inequalities for quasi-convex functions via improved power-mean inequality

In this paper, by using power-mean and improved power-mean integral inequality and an general identity for differentiable functions we can get new estimates on integral inequalities for functions whose derivatives in absolute value at certain power are quasi-convex functions. It is proved that the result obtained improved power-mean integral inequality is better than the result obtained power-mean inequality. Some applications to special means of real numbers are also given.Publisher's Versio

Inequalities for α-fractional differentiable functions

Abstract In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula

On Modified Integral Inequalities for a Generalized Class of Convexity and Applications

In this paper, we concentrate on and investigate the idea of a novel family of modified p-convex functions. We elaborate on some of this newly proposed idea’s attractive algebraic characteristics to support it. This is used to study some novel integral inequalities in the frame of the Hermite–Hadamard type. A unique equality is established for differentiable mappings. The Hermite–Hadamard inequality is extended and estimated in a number of new ways with the help of this equality to strengthen the findings. Finally, we investigate and explore some applications for some special functions. We think the approach examined in this work will further pique the interest of curious researchers

Inequalities of trapezoidal type involving generalized fractional integrals

During the last years several fractional integrals were investigated. Having this idea in mind, in the present article, some new generalized fractional integral inequalities of the trapezoidal type for –preinvex functions, which are differentiable and twice differentiable, are established. Then, by employing those results, we explore the new estimates on trapezoidal type inequalities for classical integral and Riemann–Liouville fractional integrals, respectively. Finally, we apply our new inequalities to construct inequalities involving moments of a continuous random variable