## Overview

- 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

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 207)

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## About this book

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.

## Keywords

## Table of contents (18 chapters)

## Editors and Affiliations

## About the editors

**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.

## Bibliographic Information

Book Title: Exploring Mathematical Analysis, Approximation Theory, and Optimization

Book Subtitle: 270 Years Since A.-M. Legendre’s Birth

Editors: Nicholas J. Daras, Michael Th. Rassias, Nikolaos B. Zographopoulos

Series Title: Springer Optimization and Its Applications

DOI: https://doi.org/10.1007/978-3-031-46487-4

Publisher: Springer Cham

eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

Hardcover ISBN: 978-3-031-46486-7Published: 05 January 2024

Softcover ISBN: 978-3-031-46489-8Due: 18 January 2025

eBook ISBN: 978-3-031-46487-4Published: 04 January 2024

Series ISSN: 1931-6828

Series E-ISSN: 1931-6836

Edition Number: 1

Number of Pages: VIII, 473

Number of Illustrations: 11 b/w illustrations, 13 illustrations in colour

Topics: Real Functions, Optimization, Approximations and Expansions, Functional Analysis, Operator Theory, Number Theory