In this paper, some sufficient conditions for the oscillation of all solutions of second order dynamic equations with a negative sub-linear neutral term are established. The obtained results provide a unified platform that adequately covers both discrete and continuous equations. Furthermore, it covers a wide range of equations by utilizing different time scales. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]
In this research paper, we investigate some new identifies for Sarıkaya fractional integrals which introduced by Sarıkaya and Ertugral in [20]. The fractional integral operators also have been applied to Hermite-Hadamard type integral inequalities to provide their generalized properties. Furthermore, as special cases of our main results, we present several known inequalities such as Simpson, Bullen, trapezoid for convex functions. [ABSTRACT FROM AUTHOR]
In this article we present a method to get upper bound for some integrals. The method is in connection with on a generalized trapezoidal quadrature formula. Applications for upper bounds of the elliptical integral of the first kind are presented. We compare these bounds with some previous results from the literature. [ABSTRACT FROM AUTHOR]
CONVEX functions, REAL variables, MATHEMATICS, INTEGERS, HADAMARD matrices
Abstract
In the present work, we give the definition of an s-convex functions for a convex real-valued function f defined on the set of integers Z. We state and prove the discrete Hermite-Hadamard inequality for s-convex functions by using the basics of discrete calculus (i.e. the calculus onZ). Finally,we state and prove the discrete fractional Hermite-Hadamard inequality for s-convex functions by using the basics of discrete fractional calculus. [ABSTRACT FROM AUTHOR]