Quantum Hermite-Hadamard Type Inequality and Some Estimates of Quantum Midpoint Type Inequalities for Double Integrals

Kunt, Mehmet/0000-0002-8730-5370; iscan, imdat/0000-0001-6749-0591WOS: 000462503900018In this paper, we give the correct quantum Hermite-Hadamard type inequality for the functions of two variables over finite rectangles. We provide some quantum estimates between the middle and the leftmost terms in correct quantum Hermite-Hadamard inequalities of functions of two variables using convexity and quasi-convexity on the co-ordinates

POST-QUANTUM HERMITE-JENSEN-MERCER INEQUALITIES

The Jensen-Mercer inequality, which is well known in the literature, has an important place in mathematics and related disciplines. In this work, we obtain the Hermite-Jensen-Mercer inequality for post-quantum integrals by utilizing Jensen-Mercer inequalities. Then we investigate the connections between our results and those in earlier works. Moreover, we give some examples to illustrate our main results. This is the first paper about Hermite-Jensen-Mercer inequalities for post-quantum integrals

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

Inequalities

Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field

Függvényegyenletek és egyenlőtlenségek = Functional equations and inequalities

A kutatás fő vizsgálatai függvényegyenletek és függvényegyenlőtlenségek általános elméleti kérdéseire, illetve ezek különféle matematikai, információelméleti, valószínűségszámítási, közgazdasági alkalmazásaira irányultak. Ezen belül foglalkoztunk összetett függvényeket tartalmazó függvényegyenletekkel, függvényegyenletek regularitáselméletével, függvényegyenletekre és függvényegyenlőtlenségekre vonatkozó stabilitási problémákkal, középértékekre vonatkozó összehasonlítási, egyenlőségi és homogenitási problémákkal és invariancia egyenletekkel, a konvexitás magasabb-rendű és különféle általánosításaival, a konvexitási tulajdonságok stabilitásával, valószínűségeloszlások függvényegyenletes jellemzésével, az informácimértékek jellemzésével és stabilitásával, a spektrálszintézis és spektrálanalízis csoporton és hipercsoportokon való teljesülésének szükséges és elegendő feltételeinek teljesülésével, az alavető függvényegyenletek hipercsoportokon való megoldásával, valamint operátoralgebrák, függvényalgebrák és kvantumstruktúrák megőrzési problémáinak vizsgálatával. A kutatás eredményeként 118 publikáció született, amelyből 1 monográfia, 1 szerkesztett könyv, 3 PhD értekezés, 98 referált nemzetközi folyóiratcikk, 15 pedig referált konferenciakiadványban jelent meg, és több mint 100 konferencia előadást tartottunk. | The main directions of our research were to investigate general problems of the theory of functional equations and functional inequalities, and to apply these results to various questions of other branches of mathematics, information theory, probability theory, and economics. More specifically, we dealt with functional equations involving iterates of unknown functions, with regularity theory of functional equations, with stability problems of functional equations and inequalities, with comparison, equality, and homogeneity problems and invariance equation in various classes of means, with higher-order and other types of generalizations of convexity, with stability of convexity properties, with characterization and stability of information measures, with characterizations of probability distributions, with spectral synthesis and spectral analysis on groups and hypergroups, with solution of the basic functional equations on hypergroups, with preserver problems of operator and function algebras and quantum structures. The results were published in 1 monograph. in 1 edited book, in 3 PhD dissertations, in 98 referred journal articles and in 15 referred conference proceedings article

Fractional Hermite-Hadamard integral inequalities for a new class of convex functions

Fractional integral inequality plays a significant role in pure and applied mathematicsfields. It aims to develop and extend various mathematical methods. Therefore, nowadays weneed to seek accurate fractional integral inequalities in obtaining the existence and uniqueness of thefractional methods. Besides, the convexity theory plays a concrete role in the field of fractional integralinequalities due to the behavior of its definition and properties. There is also a strong relationshipbetween convexity and symmetric theories. So, whichever one we work on, we can then apply itto the other one due to the strong correlation produced between them, specifically in the last fewdecades. First, we recall the definition ofφ-Riemann–Liouville fractional integral operators and therecently defined class of convex functions, namely the ̆σ-convex functions. Based on these, we willobtain few integral inequalities of Hermite–Hadamard’s type for a ̆σ-convex function with respectto an increasing function involving theφ-Riemann–Liouville fractional integral operator. We canconclude that all derived inequalities in our study generalize numerous well-known inequalitiesinvolving both classical and Riemann–Liouville fractional integral inequalities. Finally, application tocertain special functions are pointed out