The Perturbed Median Principle for Integral Inequalities with Applications

In this paper a perturbed version of the Median Principle introduced by the author in 'The median principle for inequalities and applications' is developed. Applications for various Riemann- Stieltjes integral and Lebesgue integral inequalities are also provided

Some Reverses of the Jensen Inequality for Functions of Selfadjoint Operators in Hilbert Spaces

Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided

Some Jensen's Type Inequalities for Twice Differentiable Functions of Selfadjoint Operators in Hilbert Spaces

Some Jensen’s type inequalities for twice differentiable functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided

Hermite-Hadamard, Hermite-Hadamard-Fejer, Dragomir-Agarwal and Pachpatte Type Inequalities for Convex Functions via Fractional Integrals

The aim of this paper is to establish Hermite-Hadamard, Hermite-Hadamard-Fej\'er, Dragomir-Agarwal and Pachpatte type inequalities for new fractional integral operators with exponential kernel. These results allow us to obtain a new class of functional inequalities which generalizes known inequalities involving convex functions. Furthermore, the obtained results may act as a useful source of inspiration for future research in convex analysis and related optimization fields.Comment: 14 pages, to appear in Journal of Computational and Applied Mathematic

Bounds for the Ratio of Two Gamma Functions

By looking back at the long history of bounding the ratio Γ(x+a)/Γ(x+b) for x>-min⁡{a,b} and a,b∈ℝ, various origins of this topic are clarified, several developed courses are followed, different results are compared, useful methods are summarized, new advances are presented, some related problems are pointed out, and related references are collected

Explicit bounds on certain integral inequalities via conformable fractional calculus

Abstract: In this paper, we present some explicit upper bounds for integral inequalities with the help of Katugampola-type conformable fractional calculus. The results have been obtained to cover the previous published studies for Gronwall-Bellman and Bihari like integral inequalities

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