Exploring Mathematical Analysis, Approximation Theory, and Optimization

This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education.
Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy's inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages.

It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.

Compiles research on various developments in mathematical analysis, approximation theory and optimization Devoted to those branches of mathematics and its applications that have been influenced Provides a historical background as it relates to Legendre's work and its association to Greece's higher education

Auteur
Nicholas J Daras is a Professor at the Department of Mathematics and Engineering Sciences of the Hellenic Military Academy. He obtained his PhD in Mathematics with the highest distinction from Université des Sciences and Techniques of Lille Flandres-Artois, Lille, France, in 1988. In 2002 he received a "best paper in mathematics Award" by the Academy of Athens. Over the years he has supervised 280 Diploma Theses, 18 Postgraduate Theses and 1 Doctoral Thesis. He has authored and edited several books. His research interests lie in complex analysis, numerical analysis, modeling and numerical simulation, universal series, holomorphic mappings in several complex variables, rational approximation, operations research, topological quantum computation, numerical representations as well as quantum cryptography and security.

Michael Th. Rassias is an Associate Professor at the Department of Mathematics and Engineering Sciences of the Hellenic Military Academy and a visiting Researcher at the Institute for Advanced Study, Princeton. He obtained his PhD in Mathematics from ETH-Zürich in 2014. During the academic year 2014 2015, he was a Postdoctoral researcher at the Department of Mathematics of Princeton University and the Department of Mathematics of ETH-Zürich, conducting research at Princeton. While at Princeton, he prepared with John F Nash, Jr. (Nobel Prize, 1994 and Abel Prize, 2015) the volume Open Problems in Mathematics, Springer, 2016. He has received several awards in mathematical problem-solving competitions, including a Silver medal at the International Mathematical Olympiad of 2003 in Tokyo. He has authored and edited several books, including the edited volume Analysis at Large jointly with A Avila (Fields Medal, 2014) and Y Sinai (Abel Prize, 2014). His current research interests lie in mathematical analysis, analytic number theory, and more specifically the Riemann Hypothesis, Goldbach's Conjecture, the distribution of prime numbers, approximation theory, functional equations, analytic inequalities and cryptography.

Nikolaos B. Zographopoulos is a Professor at the Department of Mathematics and Engineering Sciences of the Hellenic Military Academy. His research interests lie in Partial Differential Equations, Applicable Analysis and (Infinite Dimensional) Dynamical Systems.

Contenu
Preface.- On a version of Jensen-Steffensen inequality and a note on inequalities in several variables.- A class of dynamic unilateral contact problems with sub-differential friction law.- Square-free values of $[\textrm{n}^c \tan^\theta(\log \textrm{n})]$.- Ostrowski and Trapezoid Type Inequalities for Riemann-Liouville Fractional Integrals of Functions with Bounded Variation.- A strong maximum principle for general nonlinear operators.- On the Application of Ergodic Theory to an Alternating Series Expansion for Real Numbers.- Bounds for Similarity Condition Numbers of Unbounded Operators.- Legendre's Geometry and Trigonometry at the Evelpides School (Central Military School) during the Kapodristrian period.- The Overshadowing of Euclid's Geometry by Legendre's Géométrie in the Modern Greek Education.- Finite Element Methods with Higher Order Polynomials.- On Local Asymptotics for Orthonormal Polynomials.- New Trends inGeometric Function Theory.- A unified approach to extended general quasi variational inclusions.- On a Reverse Hilbert-Type Inequality in the Whole Plane with Multi-Parameters.- Generating functions for the Fubini type polynomials and their applications.- Kleene Fixed Point Theorems and Applications.- On ergodic states, spontaneous symmetry breaking and quasi-averages.- Improvement of the Hardy inequality and Legendre polynomials.