Multivariate fractional Ostrowski type inequalities

AbstractOptimal upper bounds are given for the deviation of a value of a multivariate function of a fractional space from its average, over convex and compact subsets of RN,N≥2. In particular we work over rectangles, balls and spherical shells. These bounds involve the supremum and L∞ norms of related multivariate fractional derivatives of the function involved. The inequalities produced are sharp, namely they are attained. This work has been motivated by the works of Ostrowski [A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funcktion von ihrem Integralmittelwert, Commentarii Mathematici Helvetici 10 (1938) 226–227], 1938, and of the author [G.A. Anastassiou, Fractional Ostrowski type inequalities, Communications in Applied Analysis 7 (2) (2003) 203–208], 2003

MULTIVARIATE FRACTIONAL REPRESENTATION FORMULA AND OSTROWSKI TYPE INEQUALITY

Abstract. Here we derive a multivariate fractional representation formula involving ordinary partial derivatives of first order. Then we prove a related multivariate fractional Ostrowski type inequality with respect to uniform norm

Hermite–Hadamard Type Inequalities Involving k-Fractional Operator for (h¯,m)-Convex Functions

The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established results for different kinds of convex functions are derived. This fractional integral sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have a symmetric property. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. Finally, applications of q-digamma and q -polygamma special functions are presented.This work was funded by the Basque Government for Grant IT1207-19

Nabla discrete fractional Grüss type inequality

Properties of the discrete fractional calculus in the sense of a backward difference are introduced and developed. Here, we prove a more general version of the Grüss type inequality for the nabla fractional case. An example of our main result is given

Symmetry in the Mathematical Inequalities

This Special Issue brings together original research papers, in all areas of mathematics, that are concerned with inequalities or the role of inequalities. The research results presented in this Special Issue are related to improvements in classical inequalities, highlighting their applications and promoting an exchange of ideas between mathematicians from many parts of the world dedicated to the theory of inequalities. This volume will be of interest to mathematicians specializing in inequality theory and beyond. Many of the studies presented here can be very useful in demonstrating new results. It is our great pleasure to publish this book. All contents were peer-reviewed by multiple referees and published as papers in our Special Issue in the journal Symmetry. These studies give new and interesting results in mathematical inequalities enabling readers to obtain the latest developments in the fields of mathematical inequalities. Finally, we would like to thank all the authors who have published their valuable work in this Special Issue. We would also like to thank the editors of the journal Symmetry for their help in making this volume, especially Mrs. Teresa Yu

Weighted Ostrowski type inequalities via Montgomery identity involving double integrals on time scales

In this paper, the Montgomery identity is generalized for double integrals on time scales by employing a novel analytical approach to develop the generalized Ostrowski type integral inequalities involving double integrals. Some inimitable cases are discussed for different parameters and parametric functions. Moreover, applications to some particular time scales are also presented

On the Hermite-Hadamard Inequalities for Convex Functions via Hadamard Fractional Integrals

In this paper, we establish new Hermite-Hadamard inequalitiesinvolving Hadamard fractional integrals, which are described byseries. To achieve our aim, we use fractional integral identitiesestablished, elementary inequalities in our previous works viaconvex functions and monotonicity. Finally, some applications tospecial means of real numbers are given

SciTech News Volume 70, No. 2 (2016)

Table of Contents: Columns and Reports From the Editor 3 Division News Science-Technology Division 4 New Members 6 Chemistry Division 7 New Members11 Engineering Division 12 Aerospace Section of the Engineering Division 17 Reviews Sci-Tech Book News Reviews 1