Search

The objective of this paper is to investigate and extend some Pachpatte type dynamic inequalities on time scales in three independent variables which provide explicit bounds on unknown functions and their derivatives. Some applications are also discussed here in order to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate and extend some Pachpatte type dynamic inequalities on time scales in three independent variables which provide explicit bounds on unknown functions and their derivatives. Some applications are also discussed here in order to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish several new inequalities of the Hermite-Hadamard type for functions whose derivatives are extended s-convex in the absolute value and present some applications to special means of positive real numbers. [ABSTRACT FROM AUTHOR]

In this paper, we first prove two Hermite-Hadamard type inequalities for h-preinvex functions via Riemann-Liouville fractional integrals, and then, by introducing an integral identity including the second order derivatives of a given function, we establish some Hermite-Hadamard type inequalities for functions whose second order derivatives are h-preinvex via Riemann-Liouville fractional integrals. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the Gronwall-Bellman type inequalities involving the distributional Henstock-Kurzweil integral. Moreover, an linear differential equation with distributional coefficients is considered as an application. [ABSTRACT FROM AUTHOR]

A new generalization of the Ostrowski inequality and Ostrowski type inequality for dou-ble integrals on time scales are established in this paper. Several interesting inequalities representing special cases of our general results are supplied. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some new inequalities of Simpson type for functions whose third derivatives are extended s-convex functions, and apply these inequalities to derive some inequalities of special means. [ABSTRACT FROM AUTHOR]

Several new weighted inequalities connected with Hermite-Hadamard and Fejér type inequalities are established for functions whose derivatives in absolute value are preinvex. The results presented in this paper provide ex- tensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some new inequalities of Simpson type for functions whose third derivatives are extended s-convex functions, and apply these inqualities to derive some inqualitites of special means. [ABSTRACT FROM AUTHOR]

The main object of this paper is to study some properties of certain subclass of analytic functions in the open unit disc which is defined by the linear operator ..., where Rnf(z) is the Ruscheweyh derivative, Snf(z) the Salagean operator and ... is the class of normalized analytic functions with A1 = A. These properties include a coefficient inequality, distorsion theorem and extreme points of differential operator. We also discuss the boundedness properties associated with partial sums of functions in the class .... [ABSTRACT FROM AUTHOR]

In this paper, we study some new inequalities of Hermite-Hadamard's type fractional integral inequalities for functions whose absolute values of second derivatives are convex and concave . The obtained results generalize the existing Hermite-Hadamard type integral inequalities and their application in special means and numerical integration. [ABSTRACT FROM AUTHOR]

In this paper, we study some new inequalities of Hermite-Hadamard's type fractional integral inequalities for functions whose absolute values of second derivatives are convex and concave . The obtained results generalize the existing Hermite-Hadamard type integral inequalities and their application in special means and numerical integration. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish a new integral identity and, by this identity and Hölder's inequality, discover some new Hermite-Hadamard type integral inequalities for functions whose third derivatives are (α, m)-convex. [ABSTRACT FROM AUTHOR]